Search results for: directed graphs

Authors: Behnaz Pahlousay, Farshad Kazemnejad, Elisa Palezzato, Michele Torielli

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In this paper, we study the notions of connected domination number and of outer-connected domination number for middle graphs. Indeed, we obtain tight bounds for these numbers in terms of the order of the middle graph M(G). We also compute the outer-connected domination number of some families of graphs such as star graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs and some operation on graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the outer-connected domination number of middle graphs.

Keywords: connected domination number, outer-connected dom- ination number, domination number, middle graph, nordhaus- gaddum-like relation.

Procedia PDF Downloads 36

Authors: Gete Umbrey, Saifur Rahman

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Graphs are found to be most capable in computing, and its abstract structures have been applied in some specific computations and algorithms like in phase encoding controller, processor microcontroller, and synthesis of a CMOS switching network, etc. Being motivated by these works, we develop an independent approach to study semiring structures and various properties by defining the binary operations which in fact, seems analogous to an existing definition in some sense but with a different approach. This work emphasizes specifically on the construction of semigroup and semiring structures on the set of undirected graphs, and their properties are investigated therein. It is expected that the investigation done here may have some interesting applications in theoretical computer science, networking and decision making, and also on joining of two network systems.

Keywords: graphs, join and union of graphs, semiring, weighted graphs

Procedia PDF Downloads 148

Authors: Seyed Ahmad Mojallal

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Let G be a connected threshold graph of order n with m edges and trace T. In this talk we give a lower bound on Laplacian energy in terms of n, m, and T of G. From this we determine the threshold graphs with the first four minimal Laplacian energies. We also list the first 20 minimal Laplacian energies among threshold graphs. Let σ=σ(G) be the number of Laplacian eigenvalues greater than or equal to average degree of graph G. Using this concept, we obtain the threshold graphs with the largest and the second largest Laplacian energies.

Keywords: Laplacian eigenvalues, Laplacian energy, threshold graphs, extremal graphs

Procedia PDF Downloads 386

Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell

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We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.

Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science

Procedia PDF Downloads 373

Authors: Y. Wang

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The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

Procedia PDF Downloads 231

Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

Procedia PDF Downloads 399

Authors: Swapnil Gupta, C. Pandu Rangan

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A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: uniquely restricted matching, interval graph, matching, induced matching, witness counting

Procedia PDF Downloads 388

Authors: Vadim E. Levit, Eugen Mandrescu

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A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.

Keywords: maximum independent set, corona, concatenation, join, well-covered graph

Procedia PDF Downloads 207

Authors: Robert Gold

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Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: control flow graph, graph reduction, software engineering, software applications

Procedia PDF Downloads 551

Authors: Khidir R. Sharaf, Didar A. Ali

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The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

Procedia PDF Downloads 238

Authors: Arun Prabhakar

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Threat modeling is an important activity carried out in the initial stages of the development lifecycle that helps in building proactive security measures in the product. Though there are many techniques and tools available today, one of the common challenges with the traditional methods is the lack of a systematic approach in identifying security threats. The proposed solution describes an organized model by defining ontologies that help in building patterns to enumerate threats. The concepts of graph theory are applied to build the pattern for discovering threats for any given scenario. This graph-based solution also brings in other benefits, making it a customizable and scalable model.

Keywords: directed acyclic graph, ontology, patterns, threat identification, threat modeling

Procedia PDF Downloads 137

Authors: Silmy A. Humaira'

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There is an issue about Asian students including Indonesian students that tend to behave passively in the classroom and depend on the teachers’ instruction. Regarding this statement, this study attempts to address the Indonesian high school students’ attitudes on whether they have initiative and be responsible for their learning out of the classroom and if so, why. Therefore, 30 high school students were asked to fill out the questionnaires and interviewed in order to figure out their attitudes towards self-directed learning. The descriptive qualitative research analysis adapted Knowles’s theory (1975) about Self-directed learning (SDL) to analyze the data. The findings show that the students have a potential to possess self-directed learning through ICT, but they have difficulties in choosing appropriate learning strategy, doing self-assessment and conducting self-reflection. Therefore, this study supports the teacher to promote self-directed learning instruction for successful learning by assisting students in dealing with those aforementioned problems. Furthermore, it is expected to be a beneficial reference which gives new insights on the self-directed learning practice in specific context.

Keywords: ICT, learning autonomy, students’ attitudes, self-directed learning

Procedia PDF Downloads 225

Authors: S. R. Nayaka, Putta Swamy

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Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

Procedia PDF Downloads 248

Authors: Sofia Ait Bouazza

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We consider the problem of finding a minimum identifying code in a graph. This problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of applications (fault diagnosis, location detection …). Suppose we have a building into which we need to place fire alarms. Suppose each alarm is designed so that it can detect any fire that starts either in the room in which it is located or in any room that shares a doorway with the room. We want to detect any fire that may occur or use the alarms which are sounding to not only to not only detect any fire but be able to tell exactly where the fire is located in the building. For reasons of cost, we want to use as few alarms as necessary. The first problem involves finding a minimum domination set of a graph. If the alarms are three state alarms capable of distinguishing between a fire in the same room as the alarm and a fire in an adjacent room, we are trying to find a minimum locating domination set. If the alarms are two state alarms that can only sound if there is a fire somewhere nearby, we are looking for a differentiating domination set of a graph. These three areas are the subject of much active research; we primarily focus on the third problem. An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most r≥1 from x. When only vertices out of the code are asked to be identified, we get the related concept of a locating dominating set. The problem of finding an identifying code (resp a locating dominating code) of minimum size is a NP-hard problem, even when the input graph belongs to a number of specific graph classes. Therefore, we study this problem in some restricted classes of undirected graphs like split graph, line graph and path in a directed graph. Then we present some results on the identifying code by giving an exact value of upper total locating domination and a total 2-identifying code in directed and undirected graph. Moreover we determine exact values of locating dominating code and edge identifying code of thin headless spider and locating dominating code of complete suns.

Keywords: identiying codes, locating dominating set, split graphs, thin headless spider

Procedia PDF Downloads 478

Authors: Josef Slapal

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Digital images are approximations of real ones and, therefore, to be able to study them, we need the digital plane Z2 to be equipped with a convenient structure that behaves analogously to the Euclidean topology on the real plane. In particular, it is required that such a structure allows for a digital analogue of the Jordan curve theorem. We introduce certain adjacency graphs on the digital plane and prove digital Jordan curves for them thus showing that the graphs provide convenient structures on Z2 for the study and processing of digital images. Further convenient structures including the wellknown Khalimsky and Marcus-Wyse adjacency graphs may be obtained as quotients of the graphs introduced. Since digital Jordan curves represent borders of objects in digital images, the adjacency graphs discussed may be used as background structures on the digital plane for solving the problems of digital image processing that are closely related to borders like border detection, contour filling, pattern recognition, thinning, etc.

Keywords: digital plane, adjacency graph, Jordan curve, quotient adjacency

Procedia PDF Downloads 378

Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

Procedia PDF Downloads 288

Authors: Walaa Obaidallah Alqarafi, Wafaa Mohammed Fakieh, Alaa Abdallah Altassan

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Algebraic graph theory is defined as a bridge between algebraic structures and graphs. It has several uses in many fields, including chemistry, physics, and computer science. The prime graph is a type of graph associated with a ring R, where the vertex set is the whole ring R, and two vertices x and y are adjacent if either xRy=0 or yRx=0. However, the investigation of the prime graph over rings remains relatively limited. The behavior of this graph in extended rings, like R[x] and R[[x]], where R is a non-commutative ring, deserves more attention because of the wider applicability in algebra and other mathematical fields. To study the prime graphs over polynomials and power series rings, we used a combination of ring-theoretic and graph-theoretic techniques. This paper focuses on two invariants: the diameter and the girth of these graphs. Furthermore, the work discusses how the graph structures change when passing from R to R[x] and R[[x]]. In our study, we found that the set of strong zero-divisors of ring R represents the set of vertices in prime graphs. Based on this discovery, we redefined the vertices of prime graphs using the definition of strong zero divisors. Additionally, our results show that although the prime graphs of R[x] and R[[x]] are comparable to the graph of R, they have different combinatorial characteristics since these extensions contain new strong zero-divisors. In particular, we find conditions in which the diameter and girth of the graphs, as they expand from R to R[x] and R[[x]], do not change or do change. In conclusion, this study shows how extending a non-commutative ring R to R[x] and R[[x]] affects the structure of their prime graphs, particularly in terms of diameter and girth. These findings enhance the understanding of the relationship between ring extensions and graph properties.

Keywords: prime graph, diameter, girth, polynomial ring, power series ring

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Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

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Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

Procedia PDF Downloads 231

Authors: Bin Sheng, Changhong Lu

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Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

Procedia PDF Downloads 239

Authors: Timna Mayer

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This paper explores the vast potential of self-directed learning in violin pedagogy. Based in practice and drawing on concepts from neuropsychology, the author, a violinist and teacher, outlines five learning principles. Self-directed learning is defined as an ongoing process based on problem detection, definition, and resolution. The traditional roles of teacher and student are reimagined within this context. A step-by-step guide to applied self-directed learning suggests a model for both teachers and students that realizes student independence in the classroom, leading to higher-level understanding and more robust performance. While the value of self-directed learning is well-known in general pedagogy, this paper is novel in applying the approach to the study of musical performance, a field which is currently dominated by habit and folklore, rather than informed by science.

Keywords: neuropsychology and musical performance, self-directed learning, strategic problem solving, violin pedagogy

Procedia PDF Downloads 148

Authors: Rosaline Govender

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This research study is an exploration of the self-directed professional development of teachers who teach in public schools in an era of democracy and educational change in South Africa. Amidst an ever-changing educational system, the teachers in this study position themselves as self-directed teacher-learners where they adopt particular learning practices which enable change within the broader discourses of public schooling. Life-story interviews were used to enter into the private and public spaces of five teachers which offer glimpses of how particular systems shaped their identities, and how the meanings of self-directed teacher-learner shaped their learning practices. Through the Multidimensional framework of analysis and interpretation the teachers’ stories were analysed through three lenses: restorying the field texts - the self through story; the teacher-learner in relation to social contexts, and practices of self-directed learning.This study shows that as teacher-learners learn for change through self-directed learning practices, they develop their agency as transformative intellectuals, which is necessary for the reworking of South African public schools.

Keywords: professional development, professionality, professionalism, self-directed learning

Procedia PDF Downloads 428

Authors: Mark L. Caay, Rodolfo E. Maza

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In this paper, the authors define two new variants of domination in graphs: the marriage and the divorce domination. A subset S ⊆ V (G) is said to be a marriage dominating set of G if for every e ∈ E(G), there exists a u ∈ V (G) such that u is one of the end vertex of e. A marriage dominating set S ⊆ V (G) is said to be a divorce dominating set of G if G\S is a disconnected graph. In this study, the authors present conditions of graphs for which the marriage and the divorce domination will take place and for which the two sets will coincide. Furthermore, the author gives the necessary and sufficient conditions for marriage domination to avoid divorce.

Keywords: domination, decomposition, marriage domination, divorce domination, marriage theorem

Procedia PDF Downloads 17

Authors: Nileshkumar Vishnav, Aditya Tatu

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A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

Procedia PDF Downloads 351

Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

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The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

Procedia PDF Downloads 527

Authors: Soner Nandappa D., Ahmed Mohammed Naji

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In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

Procedia PDF Downloads 548

Authors: Zheng Baichuan, Li Shenghui, Li Bingqian, Zhang Ning, Chen Kai

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Entity alignment (EA) tasks in knowledge graphs often play a pivotal role in the integration of knowledge graphs, where structural differences often exist between the source and target graphs, such as the presence or absence of attribute information and the types of attribute information (text, timestamps, images, etc.). However, most current research efforts are focused on improving alignment accuracy, often along with an increased reliance on specific structures -a dependency that inevitably diminishes their practical value and causes difficulties when facing knowledge graph alignment tasks with varying structures. Therefore, we propose a universal knowledge graph alignment approach that only utilizes the common basic structures shared by knowledge graphs. We have demonstrated through experiments that our method achieves state-of-the-art performance in fair comparisons.

Keywords: knowledge graph, entity alignment, transformer, deep learning

Procedia PDF Downloads 43

Authors: Ivan Belik

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In terms of social networks split graphs correspond to the variety of interpersonal and intergroup relations. In this paper we analyse the interaction between the cliques (socially strong and trusty groups) and the independent sets (fragmented and non-connected groups of people) as the basic components of any split graph. Based on the Semi-Lagrangean relaxation for the k-cardinality assignment problem we show the way of how to minimize the socially risky interactions between the cliques and the independent sets within the social network.

Keywords: cliques, independent sets, k-cardinality assignment, social networks, split graphs

Procedia PDF Downloads 319

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: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

Procedia PDF Downloads 398

Authors: Analen Malnegro, Gina Malacas

Abstract:

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

Procedia PDF Downloads 184