Search results for: split graphs

Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

Procedia PDF Downloads 69

Authors: Analen Malnegro, Gina Malacas

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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

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Authors: Hanan Al-Khalaifah, Afaf Al-Nasser

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The egg shell quality and oviposition in laying hens are influenced by a range of factors including strain of birds, age, nutrition, water quality, general stress, heat stress, disease, and lighting program inside houses. A layer experiment was conducted to investigate the effect of split-phase lighting program on egg production efficiency. Four different feeds and average phosphorus (av. P) levels were tested. Diet A was a ration with an av. P level of 0.471%; Diet B was a ration with an av. P level of 0.510%; Diet C contained an av. P level of 0.293%; and Diet D contained an av. P level of 0.327%. The split-phase lighting program tested was one that inserted a 7-hour dark period from 9 am to 4 pm to reduce the heat produced by the feeding increment and physical activity of the hens. Diet B produced significantly more eggs than Diet C, or Diet D. Diet A was not significantly different from any of the other diets. Diet B also had the best feed efficiency with the other three diets in the same order and significance as for egg production. Diet D produced eggshells significantly thicker than either Diet A, or Diet B. Diet C produced thicker eggshells than Diet B, whose shells were significantly thinner than the other three diets. There were no differences in egg size. From these data, it is apparent that the minimal av. P level for the Lohmann strain of layer in Kuwait is above 0.327%. There was no difference in egg production or eggshell thickness between the split-phase light treatment and the standard light program. There was no difference in oviposition frequency. The split-phase light used 3.66% less feed, however, which was significant. The standard light produced eggs that were significantly heavier (66.30g vs. 65.73g). These results indicate that considerable savings in feed costs could be attained by using split-phase lighting, especially when cooling is not very efficient.

Keywords: egg, laying, nutrition, oviposition

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Authors: Ahmed Mohamed El-Shamy, Akram Abbas El-Awady, Mahmoud Taha Eldestawy

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Background: The present study was to evaluate clinically and radiographically the combined effect of split crest technique by ultrasonic bone surgery and platelet concentrates in implant site development. Methods: Forty patients with narrow ridge were participated in this study. Patients were assigned randomly into one of the following four groups according to treatment: Group 1: Patients received split-crest technique by ultrasonic bone surgery with implant placement. Group 2: Patients received split-crest technique by ultrasonic bone surgery with implant placement and PRF. Group 3: Patients received split-crest technique by ultrasonic bone surgery with implant placement and PRP. Group 4: Patients received split-crest technique by ultrasonic bone surgery with implant placement and collagen membrane. Modified plaque index, modified sulcus bleeding index, and implant stability were recorded as a baseline and measured again at 3 and 6 months. CBCT scans were taken immediately after surgery completion and at 9 months to evaluate bone density at the bone-implant interface. Results after 6 months; collagen group showed statistically significantly lower mean modified bleeding index than the other groups. After 3 months, the PRF group showed statistically significantly higher mean implant stability with ostell ISQ units' than the other groups. After 6 months, the PRF group showed statistically significantly higher mean implant stability with ostell ISQ units' than the other groups. After 6 months, the PRF group showed statistically significantly higher mean bone density than the collagen group. Conclusion: Ultrasonic bone surgery in split-crest technique can be a successful option for increasing implant stability values throughout the healing period. The use of a combined technique of ultrasonic bone surgery with PRF and simultaneous implant placement potentially improves osseointegration (bone density). PRF membranes represent advanced technology for the stimulation and acceleration of bone regeneration.

Keywords: dental implants, split-crest, PRF, PRP

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Authors: Anteneh Getachew Gebrie, Rabian Wangkeeree

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The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

Keywords: Hilbert Space, minimization problems, Moreau-Yosida approximate, split feasibility problem

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Authors: R. K. Saket, K. S. Anand Kumar

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This paper presents an innovative 3-wire capacitor circuit system used to increase the efficiency and comfort improvement of permanent split-capacitor ceiling fan. In this innovative circuit, current has been reduced to save electrical power. The system could be used to replace standard single phase motor 2-wire capacitor configuration by cost effective split value X rated of optimized AC capacitors with the auxiliary winding to provide reliable ceiling fan operation and improved machine performance to save power. In basic system operations, comparisons with conventional ceiling fan are described.

Keywords: permanent split-capacitor motor, innovative 3-wire capacitor circuit system, standard 2-wire capacitor circuit system, metalized film X-rated capacitor

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Authors: Amira Dhokar, Lobna Hlaoua, Lotfi Ben Romdhane

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Tweet contextualization (TC) is a new issue that aims to answer questions of the form 'What is this tweet about?' The idea of this task was imagined as an extension of a previous area called multi-document summarization (MDS), which consists in generating a summary from many sources. In both TC and MDS, the summary should ideally contain the most relevant information of the topic that is being discussed in the source texts (for MDS) and related to the query (for TC). Furthermore of being informative, a summary should be coherent, i.e. well written to be readable and grammatically compact. Hence, coherence is an essential characteristic in order to produce comprehensible texts. In this paper, we propose a new approach to improve readability and coherence for tweet contextualization based on bipartite graphs. The main idea of our proposed method is to reorder sentences in a given paragraph by combining most expressive words detection and HITS (Hyperlink-Induced Topic Search) algorithm to make up a coherent context.

Keywords: bipartite graphs, readability, summarization, tweet contextualization

Procedia PDF Downloads 191

Authors: Stefan Wagenpfeil, Felix Engel, Paul McKevitt, Matthias Hemmje

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Multimedia Indexing and Retrieval is generally designed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, especially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelization. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information.

Keywords: indexing, retrieval, multimedia, graph algorithm, graph code

Procedia PDF Downloads 160

Authors: J. C. Valenzuela-Tripodoro, P. Álvarez-Ruíz, M. A. Mateos-Camacho, M. Cera

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In 2004, it was introduced the concept of Roman domination in graphs. This concept was initially inspired and related to the defensive strategy of the Roman Empire. An undefended place is a city so that no legions are established on it, whereas a strong place is a city in which two legions are deployed. This situation may be modeled by labeling the vertices of a finite simple graph with labels {0, 1, 2}, satisfying the condition that any 0-vertex must be adjacent to, at least, a 2-vertex. Roman domination in graphs is a variant of classic domination. Clearly, the main aim is to obtain such labeling of the vertices of the graph with minimum cost, that is to say, having minimum weight (sum of all vertex labels). Formally, a function f: V (G) → {0, 1, 2} is a Roman dominating function (RDF) in the graph G = (V, E) if f(u) = 0 implies that f(v) = 2 for, at least, a vertex v which is adjacent to u. The weight of an RDF is the positive integer w(f)= ∑_(v∈V)▒〖f(v)〗. The Roman domination number, γ_R (G), is the minimum weight among all the Roman dominating functions? Obviously, the set of vertices with a positive label under an RDF f is a dominating set in the graph, and hence γ(G)≤γ_R (G). In this work, we start the study of a generalization of RDF in which we consider that any undefended place should be defended from a sudden attack by, at least, k legions. These legions can be deployed in the city or in any of its neighbours. A function f: V → {0, 1, . . . , k + 1} such that f(N[u]) ≥ k + |AN(u)| for all vertex u with f(u) < k, where AN(u) represents the set of active neighbours (i.e., with a positive label) of vertex u, is called a [k]-multiple Roman dominating functions and it is denoted by [k]-MRDF. The minimum weight of a [k]-MRDF in the graph G is the [k]-multiple Roman domination number ([k]-MRDN) of G, denoted by γ_[kR] (G). First, we prove that the [k]-multiple Roman domination decision problem is NP-complete even when restricted to bipartite and chordal graphs. A problem that had been resolved for other variants and wanted to be generalized. We know the difficulty of calculating the exact value of the [k]-MRD number, even for families of particular graphs. Here, we present several upper and lower bounds for the [k]-MRD number that permits us to estimate it with as much precision as possible. Finally, some graphs with the exact value of this parameter are characterized.

Keywords: multiple roman domination function, decision problem np-complete, bounds, exact values

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Authors: Ishapathik Das

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The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs

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Authors: C. Elavarasi, T. Shanmuganantham

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A coplanar waveguide (CPW) feed is presented, and comprising a split ring resonator (SRR) loaded fractal with water lily shape is used for multi band applications. The impedance matching of the antenna is determined by the number of Koch curve fractal unit cells. The antenna is designed on a FR4 substrate with a permittivity of ε_{r =} 4.4 and size of 14 x 16 x 1.6 mm³ to generate multi resonant mode at 3.8 GHz covering S band, 8.68 GHz at X band, 13.96 GHz at Ku band, and 19.74 GHz at K band with reflection coefficient better than -10 dB. Simulation results show that the antenna exhibits the desired voltage standing wave ratio (VSWR) level and radiation patterns across the wide frequency range. The fundamental parameters of the antenna such as return loss, VSWR, good radiation pattern with reasonable gain across the operating bands are obtained.

Keywords: fractal, metamaterial, split ring resonator, waterlily shape

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Authors: Itumeleng Phage

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Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

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Authors: Prashant Malavadkar, Santosh Dhotre, Maruti Shikare

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The n-point splitting operation on graphs is used to characterize 4-connected graphs with some more operations. Element splitting operation on binary matroids is a natural generalization of the notion of n-point splitting operation on graphs. The element splitting operation on a graphic (cographic) matroid may not yield a graphic (cographic) matroid. Characterization of graphic (cographic) matroids whose element splitting matroids are graphic (cographic) is known. The element splitting operation on a co-graphic matroid, in general may not yield a graphic matroid. In this paper, we give a necessary and sufficient condition for the cographic matroid to yield a graphic matroid under the element splitting operation. In fact, we prove that the element splitting operation, by any pair of elements, on a cographic matroid yields a graphic matroid if and only if it has no minor isomorphic to M(K4); where K4 is the complete graph on 4 vertices.

Keywords: binary matroids, splitting, element splitting, forbidden minor

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Authors: Verónica Díaz

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A Cartesian graph, as a mathematical object, becomes a tool for configuration of change. Its best comprehension is done through everyday life problem-solving associated with its representation. Despite this, the current educational framework favors general graphs, without consideration of their argumentation. Students are required to find the mathematical function without associating it to the development of graphical language. This research describes the use made by students of configurations made prior to Cartesian graphs with regards to an everyday life problem related to a time and distance variation phenomenon. The theoretical framework describes the function conditions of study and their modeling. This is a qualitative, descriptive study involving six undergraduate case studies that were carried out during the first term in 2016 at University of Los Lagos. The research problem concerned the graphic modeling of a real person’s movement phenomenon, and two levels of analysis were identified. The first level aims to identify local and global graph interpretations; a second level describes the iconicity and referentiality degree of an image. According to the results, students were able to draw no figures before the Cartesian graph, highlighting the need for students to represent the context and the movement of which causes the phenomenon change. From this, they managed Cartesian graphs representing changes in position, therefore, achieved an overall view of the graph. However, the local view only indicates specific events in the problem situation, using graphic and verbal expressions to represent movement. This view does not enable us to identify what happens on the graph when the movement characteristics change based on possible paths in the person’s walking speed.

Keywords: cartesian graphs, higher education, movement modeling, problem solving

Procedia PDF Downloads 217

Authors: Hui-Chuan Lu

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In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access structures, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing a given access structure is the ratio of the average length of the shares given to the participants to the length of the secret. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing an access structure is called the optimal average information ratio of that access structure. We study the optimal average information ratio of the access structures based on bipartite graphs. Based on some previous results, we give a bound on the optimal average information ratio for all bipartite graphs of girth at least six. This bound is the best possible for some classes of bipartite graphs using our approach.

Keywords: secret-sharing scheme, average information ratio, star covering, deduction, core cluster

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Authors: Shokofeh Ebrtahimi

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Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G.Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.[1] The pioneers of the chemical graph theory are Alexandru Balaban, Ante Graovac, Ivan Gutman, Haruo Hosoya, Milan Randić and Nenad TrinajstićLet G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new program for computing the detour index of molecular graphs of nanotubes by heptagons is determineded. Some Conjectures about detour index of Molecular graphs of nanotubes is included.

Keywords: chemical graph, detour matrix, Detour index, carbon nanotube

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Authors: Subal Kar, Madhuja Ghosh, Amitesh Kumar, Arijit Majumder

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Complementary split-ring resonator (CSRR) loaded microstrip square patch antenna has been optimally designed with the help of high frequency structure simulator (HFSS). The antenna has been fabricated on the basis of the simulation design data and experimentally tested in anechoic chamber to evaluate its gain, bandwidth, efficiency and polarization characteristics. The CSRR loaded microstrip patch antenna has been found to realize significant size miniaturization (to the extent of 24%) compared to the conventional-type microstrip patch antenna both operating at the same frequency (5.2 GHz). The fabricated antenna could realize a maximum gain of 4.17 dB, 10 dB impedance bandwidth of 34 MHz, efficiency 50.73% and with maximum cross-pol of 10.56 dB down at the operating frequency. This practically designed antenna with its miniaturized size is expected to be useful for airborne and space borne applications at microwave frequency.

Keywords: split ring resonator, metamaterial, CSRR loaded patch antenna, microstrip patch antenna, LC resonator

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Authors: Zhipeng Chen, Peng Zhang, Qingyun Liu, Li Guo

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With the Internet becoming the dominant channel for business and life, many IPs are increasingly masked using web proxies for illegal purposes such as propagating malware, impersonate phishing pages to steal sensitive data or redirect victims to other malicious targets. Moreover, as Internet traffic continues to grow in size and complexity, it has become an increasingly challenging task to detect the proxy service due to their dynamic update and high anonymity. In this paper, we present an approach based on behavioral graph analysis to study the behavior similarity of web proxy users. Specifically, we use bipartite graphs to model host communications from network traffic and build one-mode projections of bipartite graphs for discovering social-behavior similarity of web proxy users. Based on the similarity matrices of end-users from the derived one-mode projection graphs, we apply a simple yet effective spectral clustering algorithm to discover the inherent web proxy users behavior clusters. The web proxy URL may vary from time to time. Still, the inherent interest would not. So, based on the intuition, by dint of our private tools implemented by WebDriver, we examine whether the top URLs visited by the web proxy users are web proxies. Our experiment results based on real datasets show that the behavior clusters not only reduce the number of URLs analysis but also provide an effective way to detect the web proxies, especially for the unknown web proxies.

Keywords: bipartite graph, one-mode projection, clustering, web proxy detection

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Authors: Abderrahim Elmoataz

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More and more contemporary applications involve data in the form of functions defined on irregular and topologically complicated domains (images, meshs, points clouds, networks, etc). Such data are not organized as familiar digital signals and images sampled on regular lattices. However, they can be conveniently represented as graphs where each vertex represents measured data and each edge represents a relationship (connectivity or certain affinities or interaction) between two vertices. Processing and analyzing these types of data is a major challenge for both image and machine learning communities. Hence, it is very important to transfer to graphs and networks many of the mathematical tools which were initially developed on usual Euclidean spaces and proven to be efficient for many inverse problems and applications dealing with usual image and signal domains. Historically, the main tools for the study of graphs or networks come from combinatorial and graph theory. In recent years there has been an increasing interest in the investigation of one of the major mathematical tools for signal and image analysis, which are Partial Differential Equations (PDEs) variational methods on graphs. The normalized p-laplacian operator has been recently introduced to model a stochastic game called tug-of-war-game with noise. Part interest of this class of operators arises from the fact that it includes, as particular case, the infinity Laplacian, the mean curvature operator and the traditionnal Laplacian operators which was extensiveley used to models and to solve problems in image processing. The purpose of this paper is to introduce and to study a new class of normalized p-Laplacian on graphs. The introduction is based on the extension of p-harmonious function introduced in as discrete approximation for both infinity Laplacian and p-Laplacian equations. Finally, we propose to use these operators as a framework for solving many inverse problems in image processing.

Keywords: normalized p-laplacian, image processing, stochastic game, inverse problems

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Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

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One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

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Authors: Nayaka S.R., Putta Swamy, Purushothama S.

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Let G=(V, E) be a graph. A dominating set S in G is a pendant dominating set if < S > contains a pendant vertex. A pendant dominating set of G which intersects every minimum pendant dominating set in G is called a transversal pendant dominating set. The minimum cardinality of a transversal pendant dominating set is called the transversal pendant domination number of G, denoted by γ_tp(G). In this paper, we begin to study this parameter. We calculate γ_tp(G) for some families of graphs. Furthermore, some bounds and relations with other domination parameters are obtained for γ_tp(G).

Keywords: dominating set, pendant dominating set, pendant domination number, transversal pendant dominating set, transversal pendant domination number

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Authors: Severino Gervacio, Velimor Almonte, Emmanuel Natalio

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A simple graph is planar if it there is a way of drawing it in the plane without edge crossings. A planar graph which is not a proper spanning subgraph of another planar graph is a maximal planar graph. We prove that for complete tripartite graphs of order at most 9, the only ones that contain a spanning maximal planar subgraph are K1,1,1, K2,2,2, K2,3,3, and K3,3,3. The main result gives a necessary and sufficient condition for the complete tripartite graph Kx,y,z to contain a spanning maximal planar subgraph.

Keywords: complete tripartite graph, graph, maximal planar graph, planar graph, subgraph

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Authors: Sreedevi P. Chakyar, Jolly Andrews, V. P. Joseph

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A compact method for measuring the relative permittivity of a dielectric material at different temperatures using a single circular Split Ring Resonator (SRR) metamaterial unit working as a test probe is presented in this paper. The dielectric constant of a material is dependent upon its temperature and the LC resonance of the SRR depends on its dielectric environment. Hence, the temperature of the dielectric material in contact with the resonator influences its resonant frequency. A single SRR placed between transmitting and receiving probes connected to a Vector Network Analyser (VNA) is used as a test probe. The dependence of temperature between 30 ^oC and 60 ^oC on resonant frequency of SRR is analysed. Relative permittivities ‘ε’ of test samples for different temperatures are extracted from a calibration graph drawn between the relative permittivity of samples of known dielectric constant and their corresponding resonant frequencies. This method is found to be an easy and efficient technique for analysing the temperature dependent permittivity of different materials.

Keywords: metamaterials, negative permeability, permittivity measurement techniques, split ring resonators, temperature dependent dielectric constant

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Authors: A. Kulandai Therese

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The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs.

Keywords: corona graph, degree, eccentricity, eccentric connectivity index, first zagreb index, second zagreb index, subdivision graphs

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Authors: Nileshkumar Vaishnav, Aditya Tatu

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An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing

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Authors: Amadou Fall Dia, Maurras Ulbricht Togbe, Aliou Boly, Zakia Kazi Aoul, Elisabeth Metais

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Existing RDF (Resource Description Framework) Stream Processing (RSP) systems allow continuous processing of RDF data issued from different application domains such as weather station measuring phenomena, geolocation, IoT applications, drinking water distribution management, and so on. However, processing window phase often expires before finishing the entire session and RSP systems immediately delete data streams after each processed window. Such mechanism does not allow optimized exploitation of the RDF data streams as the most relevant and pertinent information of the data is often not used in a due time and almost impossible to be exploited for further analyzes. It should be better to keep the most informative part of data within streams while minimizing the memory storage space. In this work, we propose an RDF graph summarization system based on an explicit and implicit expressed needs through three main approaches: (1) an approach for user queries (SPARQL) in order to extract their needs and group them into a more global query, (2) an extension of the closeness centrality measure issued from Social Network Analysis (SNA) to determine the most informative parts of the graph and (3) an RDF graph summarization technique combining extracted user query needs and the extended centrality measure. Experiments and evaluations show efficient results in terms of memory space storage and the most expected approximate query results on summarized graphs compared to the source ones.

Keywords: centrality measures, RDF graphs summary, RDF graphs stream, SPARQL query

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Authors: Akansha Tyagi, Mehar S. Sidhu, Ankur Mandal, Sanjay Kapoor, Sunil Dahiya, Jan M. Rost, Thomas Pfeifer, Kamal P. Singh

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An all-reflective split and delay unit is designed for dispersion free measurement of broadband ultrashort pulses using a pair of reflective knife edge prism for splitting and recombining of the measuring pulse. It is based on symmetrical wavefront splitting of the measuring pulse having two separate arms to independently shape both split parts. We have validated our delay line with NIR –femtosecond pulse measurement centered at 800 nm using second harmonic-Interferometric frequency resolved optical gating (SH-IFROG). The delay line is compact, easy to align and provides attosecond stability and precision and thus make it more versatile for wide range of applications in ultrafast measurements. We envision that the present delay line will find applications in IR-IR controlling for high harmonic generation (HHG) and attosecond IR-XUV pump-probe measurements with solids and gases providing attosecond resolution and wide delay range.

Keywords: HHG, nonlinear optics, pump-probe spectroscopy, ultrafast metrology

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Authors: Amrit Pal Singh Arora

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The paper reports the results of a study undertaken to study the effects of addition of steel fibres of different aspect ratios on the permeability and strength characteristics of steel fiber reinforced fly ash concrete (SFRC). Corrugated steel fibres having a diameter of 0.6 mm and lengths of 12.5 mm, 30 mm and 50 mm were used in this study. Cube samples of 100 mm x 100 mm x 100 mm were cast from mixes replacing 0%, 10%, 20% and 30% cement content by fly ash with and without fibres and tested for the determination of coefficient of water permeability, compressive and split tensile strengths after 7 and 28 days of curing. Plain concrete samples were also cast and tested for reference purposes. Permeability was observed to decrease significantly for all concrete mixes with the addition of steel fibers as compared to plain concrete. The replacement of cement content by fly ash results in an increase in the coefficient of water permeability. With the addition of fly ash to the plain mix the7 day compressive and split tensile strengths decreased, however both the compressive and split tensile strengths increased with increase in curing age.

Keywords: curing age, fiber shape, fly ash, Darcy’s law, Ppermeability

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Authors: Marianna Bolla

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The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.

Keywords: generalized random graphs, multiway discrepancy, normalized modularity spectra, spectral clustering

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Authors: Zainab Yasir Abed Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel

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