Search results for: structural graph

Authors: Zhihao Zheng, Zhilin Wang, Linxin Liu

Abstract:

In the research of automated knowledge question-answering systems, accuracy and efficiency are critical challenges. This paper proposes a knowledge graph-enhanced Retrieval-Augmented Generation (RAG) method, combined with a Graph Neural Network (GNN) structure, to automatically determine the correctness of knowledge competition questions. First, a domain-specific knowledge graph was constructed from a large corpus of academic journal literature, with key entities and relationships extracted using Natural Language Processing (NLP) techniques. Then, the RAG method's retrieval module was expanded to simultaneously query both text databases and the knowledge graph, leveraging the GNN to further extract structured information from the knowledge graph. During answer generation, contextual information provided by the knowledge graph and GNN is incorporated to improve the accuracy and consistency of the answers. Experimental results demonstrate that the knowledge graph and GNN-enhanced RAG method perform excellently in determining the correctness of questions, achieving an accuracy rate of 95%. Particularly in cases involving ambiguity or requiring contextual information, the structured knowledge provided by the knowledge graph and GNN significantly enhances the RAG method's performance. This approach not only demonstrates significant advantages in improving the accuracy and efficiency of automated knowledge question-answering systems but also offers new directions and ideas for future research and practical applications.

Keywords: knowledge graph, graph neural network, retrieval-augmented generation, NLP

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

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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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Authors: Gerardo Ayala-Jaimes, Gilberto Gonzalez-Avalos, Allen A. Castillo, Alejandra Jimenez

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The modeling of a single-phase cycloconverter in Bond Graph is presented, which includes an alternating current power supply, hybrid dynamics, switch control, and resistive load; this approach facilitates the integration of systems across different energy domains and structural analysis. Cycloconverters, used in motor control, demonstrate the viability of graphical modeling. The use of Bonds is proposed to model the hybrid interaction of the system, and the results are displayed through simulations using 20Sim and Multisim software. The motivation behind developing these models with a graphical approach is to design and build low-cost energy converters, thereby making the main contribution of this document the modeling and simulation of a single-phase cycloconverter.

Keywords: bond graph, hybrid system, rectifier, cycloconverter, modelling

Procedia PDF Downloads 36

Authors: David Pham, Yongfeng Zhang

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Graphs are an important structure for data storage and computation. Recent years have seen the success of deep learning on graphs such as Graph Neural Networks (GNN) on various data mining and machine learning tasks. However, most of the deep learning models on graphs cannot easily explain their predictions and are thus often labelled as “black boxes.” For example, Graph Attention Network (GAT) is a frequently used GNN architecture, which adopts an attention mechanism to carefully select the neighborhood nodes for message passing and aggregation. However, it is difficult to explain why certain neighbors are selected while others are not and how the selected neighbors contribute to the final classification result. In this paper, we present a graph learning model called Explainable Graph Attention Network (XGAT), which integrates graph attention modeling and explainability. We use a single model to target both the accuracy and explainability of problem spaces and show that in the context of graph attention modeling, we can design a unified neighborhood selection strategy that selects appropriate neighbor nodes for both better accuracy and enhanced explainability. To justify this, we conduct extensive experiments to better understand the behavior of our model under different conditions and show an increase in both accuracy and explainability.

Keywords: explainable AI, graph attention network, graph neural network, node classification

Procedia PDF Downloads 197

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

Abstract:

Coloring 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 W14 is chromatically unique.

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

Procedia PDF Downloads 410

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 41

Authors: Ould Bouamama, M. Bressel, D. Hissel, M. Hilairet

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Fuel cell (FC) is one of the best alternatives of fossil energy. Recently, the research community of fuel cell has shown a considerable interest for diagnosis in view to ensure safety, security, and availability when faults occur in the process. The problematic for model based FC diagnosis consists in that the model is complex because of coupling of several kind of energies and the numerical values of parameters are not always known or are uncertain. The present paper deals with use of one tool: the Linear Fractional Transformation bond graph tool not only for uncertain modelling but also for monitorability (ability to detect and isolate faults) analysis and formal generation of robust fault indicators with respect to parameter uncertainties.The developed theory applied to a nonlinear FC system has proved its efficiency.

Keywords: bond graph, fuel cell, fault detection and isolation (FDI), robust diagnosis, structural analysis

Procedia PDF Downloads 363

Authors: Junjie Zhong, Kai Hong, Lei Wang

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Passage Retrieval (PR) plays an important role in many Natural Language Processing (NLP) tasks. Traditional efficient retrieval models relying on exact term-matching, such as TF-IDF or BM25, have nowadays been exceeded by pre-trained language models which match by semantics. Though they gain effectiveness, deep language models often require large memory as well as time cost. To tackle the trade-off between efficiency and effectiveness in PR, this paper proposes Graph Passage Retriever (GraphPR), a graph-based model inspired by the development of graph learning techniques. Different from existing works, GraphPR is end-to-end and integrates both term-matching information and semantics. GraphPR constructs a passage-level graph from BM25 retrieval results and trains a GCN-like model on the graph with graph-based objectives. Passages were regarded as nodes in the constructed graph and were embedded in dense vectors. PR can then be implemented using embeddings and a fast vector-similarity search. Experiments on a variety of real-world retrieval datasets show that the proposed model outperforms related models in several evaluation metrics (e.g., mean reciprocal rank, accuracy, F1-scores) while maintaining a relatively low query latency and memory usage.

Keywords: efficiency, effectiveness, graph learning, language model, passage retrieval, term-matching model

Procedia PDF Downloads 145

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

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Authors: Shuo Liu

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In Chinese text classification tasks, redundant words and phrases can interfere with the formation of extracted and analyzed text information, leading to a decrease in the accuracy of the classification model. To reduce irrelevant elements, extract and utilize text content information more efficiently and improve the accuracy of text classification models. In this paper, the text in the corpus is first extracted using the TextRank algorithm for abstraction, the words in the abstract are used as nodes to construct a text graph, and then the graph attention network (GAT) is used to complete the task of classifying the text. Testing on a Chinese dataset from the network, the classification accuracy was improved over the direct method of generating graph structures using text.

Keywords: Chinese natural language processing, text classification, abstract extraction, graph attention network

Procedia PDF Downloads 99

Authors: Mehrshad Khosraviani, Sepehr Najjarpour

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Considering the usage of graph-based approaches in systems and synthetic biology, and the various types of ‎the graphs employed by them, a comprehensive graph library based ‎on the three-tier architecture (3TA) was previously introduced for full representation of the biological systems. Although proposing a 3TA-based graph library, three following reasons motivated us to redesign the graph ‎library based on the service-oriented architecture (SOA): (1) Maintaining the accuracy of the data related to an input graph (including its edges, its ‎vertices, its topology, etc.) without involving the end user:‎ Since, in the case of using 3TA, the library files are available to the end users, they may ‎be utilized incorrectly, and consequently, the invalid graph data will be provided to the ‎computer algorithms. However, considering the usage of the SOA, the operation of the ‎graph registration is specified as a service by encapsulation of the library files. In other words, overall control operations needed for registration of the valid data will be the ‎responsibility of the services. (2) Partitioning of the library product into some different parts: Considering 3TA, a whole library product was provided in general. While here, the product ‎can be divided into smaller ones, such as an AND/OR graph drawing service, and each ‎one can be provided individually. As a result, the end user will be able to select any ‎parts of the library product, instead of all features, to add it to a project. (3) Reduction of the complexities: While using 3TA, several other libraries must be needed to add for connecting to the ‎database, responsibility of the provision of the needed library resources in the SOA-‎based graph library is entrusted with the services by themselves. Therefore, the end user ‎who wants to use the graph library is not involved with its complexity. In the end, in order to ‎make ‎the library easier to control in the system, and to restrict the end user from accessing the files, ‎it was preferred to use the service-oriented ‎architecture ‎‎(SOA) over the three-tier architecture (3TA) and to redevelop the previously proposed graph library based on it‎.

Keywords: Bio-Design Automation, Biological System, Graph Library, Service-Oriented Architecture, Systems and Synthetic Biology

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Authors: Shaowei Sun

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Let G be a graph with vertex set V(G)={v_1,v_2,...,v_n} and edge set E(G). For any vertex v belong to V(G), let d_v denote the degree of v. The normalized Laplacian matrix of the graph G is the matrix where the non-diagonal (i,j)-th entry is -1/(d_id_j) when vertex i is adjacent to vertex j and 0 when they are not adjacent, and the diagonal (i,i)-th entry is the di. In this paper, we discuss some bounds on the largest and the second smallest normalized Laplacian eigenvalue of trees and graphs. As following, we found some new bounds on the second smallest normalized Laplacian eigenvalue of tree T in terms of graph parameters. Moreover, we use Sage to give some conjectures on the second largest and the third smallest normalized eigenvalues of graph.

Keywords: graph, normalized Laplacian eigenvalues, normalized Laplacian matrix, tree

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Authors: Alfi Y. Zakiyyah, Hanni Garminia, M. Salman, A. N. Irawati

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In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.

Keywords: connectivity, graph, hypergraph, Laplacian matrix

Procedia PDF Downloads 487

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: 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: Sarah E. Nelson, Casey Weiner, Alexander Sigmon, Jun Hua, Haris I. Sair, Jose I. Suarez, Robert D. Stevens

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Graph-theoretical information from structural connectomes indicated significant connectivity changes and improved acute prognostication in a Random Forest (RF) model in aneurysmal subarachnoid hemorrhage (aSAH), which can lead to significant morbidity and mortality and has traditionally been fraught by poor methods to predict outcome. This study’s hypothesis was that structural connectivity changes occur in canonical brain networks of acute aSAH patients, and that these changes are associated with functional outcome at six months. In a prospective cohort of patients admitted to a single institution for management of acute aSAH, patients underwent diffusion tensor imaging (DTI) as part of a multimodal MRI scan. A weighted undirected structural connectome was created of each patient’s images using Constant Solid Angle (CSA) tractography, with 176 regions of interest (ROIs) defined by the Johns Hopkins Eve atlas. ROIs were sorted into four networks: Default Mode Network, Executive Control Network, Salience Network, and Whole Brain. The resulting nodes and edges were characterized using graph-theoretic features, including Node Strength (NS), Betweenness Centrality (BC), Network Degree (ND), and Connectedness (C). Clinical (including demographics and World Federation of Neurologic Surgeons scale) and graph features were used separately and in combination to train RF and Logistic Regression classifiers to predict two outcomes: dichotomized modified Rankin Score (mRS) at discharge and at six months after discharge (favorable outcome mRS 0-2, unfavorable outcome mRS 3-6). A total of 56 aSAH patients underwent DTI a median (IQR) of 7 (IQR=8.5) days after admission. The best performing model (RF) combining clinical and DTI graph features had a mean Area Under the Receiver Operator Characteristic Curve (AUROC) of 0.88 ± 0.00 and Area Under the Precision Recall Curve (AUPRC) of 0.95 ± 0.00 over 500 trials. The combined model performed better than the clinical model alone (AUROC 0.81 ± 0.01, AUPRC 0.91 ± 0.00). The highest-ranked graph features for prediction were NS, BC, and ND. These results indicate reorganization of the connectome early after aSAH. The performance of clinical prognostic models was increased significantly by the inclusion of DTI-derived graph connectivity metrics. This methodology could significantly improve prognostication of aSAH.

Keywords: connectomics, diffusion tensor imaging, graph theory, machine learning, subarachnoid hemorrhage

Procedia PDF Downloads 188

Authors: Kay Thi Yar, Khin Mar Lar Tun

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Nowadays, social networks are so popular and widely used in all over the world. In addition, searching personal information of each person and searching connection between them (peoples’ relation in real world) becomes interesting issue in our society. In this paper, we propose a framework with three portions for exploring peoples’ relations from their connected information. The first portion focuses on the Graph database structure to store the connected data of peoples’ information. The second one proposes the graph database searching algorithm, the Modified-SoS-ACO (Sense of Smell-Ant Colony Optimization). The last portion proposes the Deductive Reasoning Algorithm to define two persons’ relationship. This study reveals the proper storage structure for connected information, graph searching algorithm and deductive reasoning algorithm to predict and analyze the personnel relationship from peoples’ relation in their connected information.

Keywords: personnel information, graph storage structure, graph searching algorithm, deductive reasoning algorithm

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Authors: Amir Bahrami

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In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index or a descriptor index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper some descriptor index (descriptor index) of single-walled carbon nanotubes, is determined.

Keywords: chemical graph theory, molecular topology, molecular descriptor, single-walled carbon nanotubes

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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: Yingqi Cui, Changran Huang, Raymond Lee

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In this paper, we proposed an AI Tutor using ontology and natural language process techniques to generate a computer science domain knowledge graph and answer users’ questions based on the knowledge graph. We define eight types of relation to extract relationships between entities according to the computer science domain text. The AI tutor is separated into two agents: learning agent and Question-Answer (QA) agent and developed on JADE (a multi-agent system) platform. The learning agent is responsible for reading text to extract information and generate a corresponding knowledge graph by defined patterns. The QA agent can understand the users’ questions and answer humans’ questions based on the knowledge graph generated by the learning agent.

Keywords: artificial intelligence, natural Language processing, knowledge graph, intelligent agents, QA system

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Authors: Mustafa Elfituri, Jonathan Cook

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Recently, graph-based computations have become more important in large-scale scientific computing as they can provide a methodology to model many types of relations between independent objects. They are being actively used in fields as varied as biology, social networks, cybersecurity, and computer networks. At the same time, graph problems have some properties such as irregularity and poor locality that make their performance different than regular applications performance. Therefore, parallelizing graph algorithms is a hard and challenging task. Initial evidence is that standard computer architectures do not perform very well on graph algorithms. Little is known exactly what causes this. The Graph500 benchmark is a representative application for parallel graph-based computations, which have highly irregular data access and are driven more by traversing connected data than by computation. In this paper, we present results from analyzing the performance of various example implementations of Graph500, including a shared memory (OpenMP) version, a distributed (MPI) version, and a hybrid version. We measured and analyzed all the factors that affect its performance in order to identify possible changes that would improve its performance. Results are discussed in relation to what factors contribute to performance degradation.

Keywords: graph computation, graph500 benchmark, parallel architectures, parallel programming, workload characterization.

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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 238

Authors: Rihab Ben Lamine, Raoudha Ben Jemaa, Ikram Amous Ben Amor

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This paper proposes a graph planning technique for semantic adaptable Web Services composition. First, we use an ontology based context model for extending Web Services descriptions with information about the most suitable context for its use. Then, we transform the composition problem into a semantic context aware graph planning problem to build the optimal service composition based on user's context. The construction of the planning graph is based on semantic context aware Web Service discovery that allows for each step to add most suitable Web Services in terms of semantic compatibility between the services parameters and their context similarity with the user's context. In the backward search step, semantic and contextual similarity scores are used to find best composed Web Services list. Finally, in the ranking step, a score is calculated for each best solution and a set of ranked solutions is returned to the user.

Keywords: semantic web service, web service composition, adaptation, context, graph planning

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Authors: Shin-Shin Kao, Hsiu-Chunj Pan

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Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3-ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered [1]. Furthermore, based on computer experimental results in [1], it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

Keywords: Hamiltonian cycle, 4-ordered, Chordal rings, 3-regular

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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

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Authors: Wongsakorn Charoenpanitseri

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The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: total colorings, the total chromatic number, 3-degenerated, CLAW-FREE

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Authors: Haffaf Hafid

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Hypergraphs, after being used to model the structural organization of System of Sytems (SoS) at macroscopic level, has recent trends towards generalizing this powerful representation at different stages of complex system modelling. In this paper, we first describe different applications of hypergraph theory, and step by step, introduce multilevel modeling of SoS by means of integrating Constraint Programming Langages (CSP) dealing with engineering system reconfiguration strategy. As an application, we give an A.C.T Terminal controlled by a set of Intelligent Automated Vehicle.

Keywords: hypergraph model, structural analysis, bipartite graph, monitoring, system of systems, reconfiguration analysis, hypernetwork

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Authors: Mostafa Gamal, Hoda K. Mohamed, Islam El-Maddah, Ali Hamdi

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In recent years, many digital documents on the web have been created due to the rapid growth of ’social applications’ communities or ’Data-intensive applications’. The evolution of online-based multimedia data poses new challenges in storing and querying large amounts of data for online recommender systems. Graph data models have been shown to be more efficient than relational data models for processing complex data. This paper will explain the key differences between graph and relational databases, their strengths and weaknesses, and why using graph databases is the best technology for building a realtime recommendation system. Also, The paper will discuss several similarity metrics algorithms that can be used to compute a similarity score of pairs of nodes based on their neighbourhoods or their properties. Finally, the paper will discover how NLP strategies offer the premise to improve the accuracy and coverage of realtime recommendations by extracting the information from the stored unstructured knowledge, which makes up the bulk of the world’s data to enrich the graph database with this information. As the size and number of data items are increasing rapidly, the proposed system should meet current and future needs.

Keywords: graph databases, NLP, recommendation systems, similarity metrics

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Authors: Roya Khajepour, Alireza B. Novinzadeh

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In this paper, the spherical robot is modeled using the Band-Graph approach. This breed of robots is typically employed in expedition missions to unknown territories. Its motion mechanism is based on convection of a fluid in a set of three donut vessels, arranged orthogonally in space. This robot is a non-linear, non-holonomic system. This paper utilizes the Band-Graph technique to derive the torque generation mechanism in a spherical robot. Eventually, this paper describes the motion of a sphere due to the exerted torque components.

Keywords: spherical robot, Band-Graph, modeling, torque

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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 476