Search results for: entity relation graph

Authors: Zhifei Hu, Feng Xia

Abstract:

In recent years, Graph neural network has been widely used in knowledge graph recommendation. The existing recommendation methods based on graph neural network extract information from knowledge graph through entity and relation, which may not be efficient in the way of information extraction. In order to better propose useful entity information for the current recommendation task in the knowledge graph, we propose an end-to-end Neural network Model based on multi-stream graph attentional Mechanism (MSGAT), which can effectively integrate the knowledge graph into the recommendation system by evaluating the importance of entities from both users and items. Specifically, we use the attention mechanism from the user's perspective to distil the domain nodes information of the predicted item in the knowledge graph, to enhance the user's information on items, and generate the feature representation of the predicted item. Due to user history, click items can reflect the user's interest distribution, we propose a multi-stream attention mechanism, based on the user's preference for entities and relationships, and the similarity between items to be predicted and entities, aggregate user history click item's neighborhood entity information in the knowledge graph and generate the user's feature representation. We evaluate our model on three real recommendation datasets: Movielens-1M (ML-1M), LFM-1B 2015 (LFM-1B), and Amazon-Book (AZ-book). Experimental results show that compared with the most advanced models, our proposed model can better capture the entity information in the knowledge graph, which proves the validity and accuracy of the model.

Keywords: graph attention network, knowledge graph, recommendation, information propagation

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Authors: Paolo Fantozzi, Luigi Laura, Umberto Nanni

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The problem of Entity relation discovery in structured data, a well covered topic in literature, consists in searching within unstructured sources (typically, text) in order to find connections among entities. These can be a whole dictionary, or a specific collection of named items. In many cases machine learning and/or text mining techniques are used for this goal. These approaches might be unfeasible in computationally challenging problems, such as processing massive data streams. A faster approach consists in collecting the cooccurrences of any two words (entities) in order to create a graph of relations - a cooccurrence graph. Indeed each cooccurrence highlights some grade of semantic correlation between the words because it is more common to have related words close each other than having them in the opposite sides of the text. Some authors have used sliding windows for such problem: they count all the occurrences within a sliding windows running over the whole text. In this paper we generalise such technique, coming up to a Weighted-Distance Sliding Window, where each occurrence of two named items within the window is accounted with a weight depending on the distance between items: a closer distance implies a stronger evidence of a relationship. We develop an experiment in order to support this intuition, by applying this technique to a data set consisting in the text of the Bible, split into verses.

Keywords: cooccurrence graph, entity relation graph, unstructured text, weighted distance

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Authors: Qin Long, Li Xiaoge

Abstract:

The Knowledge Graphs have now become a new form of knowledge representation. However, there is no consensus in regard to a plausible and definition of entities and relationships in the domain-specific knowledge graph. Further, in conjunction with several limitations and deficiencies, various domain-specific entities and relationships recognition approaches are far from perfect. Specifically, named entity recognition in Chinese domain is a critical task for the natural language process applications. However, a bottleneck problem with Chinese named entity recognition in new domains is the lack of annotated data. To address this challenge, a domain distant supervised named entity recognition framework is proposed. The framework is divided into two stages: first, the distant supervised corpus is generated based on the entity linking model of graph attention neural network; secondly, the generated corpus is trained as the input of the distant supervised named entity recognition model to train to obtain named entities. The link model is verified in the ccks2019 entity link corpus, and the F1 value is 2% higher than that of the benchmark method. The re-pre-trained BERT language model is added to the benchmark method, and the results show that it is more suitable for distant supervised named entity recognition tasks. Finally, it is applied in the computer field, and the results show that this framework can obtain domain named entities.

Keywords: distant named entity recognition, entity linking, knowledge graph, graph attention neural network

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Authors: Yuhong Zhang, Dan Lu, Chenyang Bu, Peipei Li, Kui Yu, Xindong Wu

Abstract:

The Cross-Lingual Entity Alignment (CLEA) task aims to find the aligned entities that refer to the same identity from two knowledge graphs (KGs) in different languages. It is an effective way to enhance the performance of data mining for KGs with scarce resources. In real-world applications, the neighborhood structures of the same entities in different KGs tend to be non-isomorphic, which makes the representation of entities contain diverse semantic information and then poses a great challenge for CLEA. In this paper, we try to address this challenge from two perspectives. On the one hand, the cross-KG relation completion rules are designed with the alignment constraint of entities and relations to improve the topology isomorphism of two KGs. On the other hand, a representation method combining isomorphic weights is designed to include more isomorphic semantics for counterpart entities, which will benefit the CLEA. Experiments show that our model can improve the isomorphism of two KGs and the alignment performance, especially for two non-isomorphic KGs.

Keywords: knowledge graphs, cross-lingual entity alignment, non-isomorphic, relation completion

Procedia PDF Downloads 107

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

Abstract:

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

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Authors: Nileshkumar Vishnav, Aditya Tatu

Abstract:

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

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

Abstract:

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

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Authors: Kay Thi Yar, Khin Mar Lar Tun

Abstract:

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: U. Mary

Abstract:

Let be a graph with a finite, nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of called edges. The vertex set is denoted by and the edge set by. Given two graphs and the wiener index of, wiener index for the splitting graph of a graph, the first Zagreb index of and its splitting graph, the 3-steiner wiener index of, the 3-steiner wiener index of a special graph are explored in this paper.

Keywords: complementary prism graph, first Zagreb index, neighborhood corona graph, steiner distance, splitting graph, steiner wiener index, wiener index

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Authors: Prateek Chharia, Biswa Bhusan Ghosh

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Graph coloring is one of the prominent concepts in graph coloring. It can be defined as a coloring of the various regions of the graph such that all the constraints are fulfilled. In this paper various graphs coloring approaches like greedy coloring, Heuristic search for maximum independent set and graph coloring using edge table is described. Graph coloring can be used in various real time applications like student time tabling generation, Sudoku as a graph coloring problem, GSM phone network.

Keywords: graph coloring, greedy coloring, heuristic search, edge table, sudoku as a graph coloring problem

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Authors: Mehmet Hakan Karaata

Abstract:

In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Asraful Islam

Abstract:

Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly.

Keywords: normal logic program, isomorphism of graph, extended labelled dependency graph, inverse graph transforma-tion, graph colouring

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Authors: Severino Gervacio, Velimor Almonte, Emmanuel Natalio

Abstract:

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: Zaqiatul Mardiah, Afdol Tharik Wastono, Abdul Muta'ali

Abstract:

In general, the Arabic preposition ‘ala encodes the sense of UP-DOWN schema. However, the use of the preposition ‘ala can has many extended schemas that still have relation to its primary sense. In this paper, we show how the framework of cognitive linguistics (CL) based on image schemas can be applied to analyze the spatial semantic of the use of preposition ‘ala in the horizontal and vertical axes. The preposition ‘ala is usually used in the locative sense in which one physical entity is UP-DOWN relation to another physical entity. In spite of that, the cognitive analysis of ‘ala justifies the use of this preposition in many situations to seemingly encode non-up down-related spatial relations, and non-physical relation. This uncovers some of the unsolved issues concerning prepositions in general and the Arabic prepositions in particular the use of ‘ala as a sample. Using the Arabic corpus data, we reveal that in many cases and situations, the use of ‘ala is extended to depict relations other than the ones where the Trajector (TR) is actually in up-down relation to the Landmark (LM). The instances analyzed in this paper show that ‘ala encodes not only the spatial relations in which the TR and the LM are horizontally or vertically related to each other, but also non-spatial relations.

Keywords: image schema, preposition, spatial semantic, up-down relation

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Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

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: Yihao Kuang, Bowen Ding

Abstract:

With the increasing scale and complexity of knowledge graph, modern knowledge graph contains more and more types of entity, relationship, and attribute information. Therefore, in recent years, it has been a trend for knowledge graph inference to use reinforcement learning to deal with large-scale, incomplete, and noisy knowledge graph and improve the inference effect and interpretability. The Proximal Policy Optimization (PPO) algorithm utilizes a near-end strategy optimization approach. This allows for more extensive updates of policy parameters while constraining the update extent to maintain training stability. This characteristic enables PPOs to converge to improve strategies more rapidly, often demonstrating enhanced performance early in the training process. Furthermore, PPO has the advantage of offline learning, effectively utilizing historical experience data for training and enhancing sample utilization. This means that even with limited resources, PPOs can efficiently train for reinforcement learning tasks. Based on these characteristics, this paper aims to obtain better and more efficient inference effect by introducing PPO into knowledge inference technology.

Keywords: reinforcement learning, PPO, knowledge inference, supervised learning

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

Abstract:

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

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Authors: M. Hussain, Aqsa Farooq

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Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.

Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph

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Authors: Qiuyi Lyu, Bin Gong

Abstract:

Breadth-First Search(BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improve the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads. We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15.

Keywords: breadth-first search, BFS, graph ordering, graph algorithm

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Authors: Yingqi Cui, Changran Huang, Raymond Lee

Abstract:

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: Gowtham Kalkere Jayanna, Mohamad Nazri Husin

Abstract:

Graph theory, chemistry, and technology are all combined in cheminformatics. The structure and physiochemical properties of organic substances are linked using some useful graph invariants and the corresponding molecular graph. In this paper, we study specific reverse topological indices such as the reverse sum-connectivity index, the reverse Zagreb index, the reverse arithmetic-geometric, and the geometric-arithmetic, the reverse Sombor, the reverse Nirmala indices for the bistar graphs B (n: m) and the corona product Kₘ∘Kₙ', where Kₙ' Represent the complement of a complete graph Kₙ.

Keywords: reverse topological indices, bistar graph, the corona product, graph

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Authors: Sanju Vaidya, Aihua Li

Abstract:

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: Mustafa Elfituri, Jonathan Cook

Abstract:

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.

Procedia PDF Downloads 127

Authors: Yihao Kuang, Bowen Ding

Abstract:

With the increasing scale and complexity of knowledge graph, modern knowledge graph contains more and more types of entity, relationship, and attribute information. Therefore, in recent years, it has been a trend for knowledge graph inference to use reinforcement learning to deal with large-scale, incomplete, and noisy knowledge graphs and improve the inference effect and interpretability. The Proximal Policy Optimization (PPO) algorithm utilizes a near-end strategy optimization approach. This allows for more extensive updates of policy parameters while constraining the update extent to maintain training stability. This characteristic enables PPOs to converge to improved strategies more rapidly, often demonstrating enhanced performance early in the training process. Furthermore, PPO has the advantage of offline learning, effectively utilizing historical experience data for training and enhancing sample utilization. This means that even with limited resources, PPOs can efficiently train for reinforcement learning tasks. Based on these characteristics, this paper aims to obtain a better and more efficient inference effect by introducing PPO into knowledge inference technology.

Keywords: reinforcement learning, PPO, knowledge inference

Procedia PDF Downloads 216

Authors: S. R. Nayaka, Putta Swamy

Abstract:

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

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Authors: Hossein Pourali

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In this paper, we extend the concepts of primal and weakly primal ideals for posets. Further, the diameter of the zero divisor graph of a poset with respect to a non-primal ideal is determined. The relation between primary and primal ideals in posets is also studied.

Keywords: ‎associated prime ideal, ‎‎ideal, ‎‎primary ideal, primal ideal‎, prime‎ ‎ideal, semiprime ideal, ‎weakly primal ideal, zero divisors graph

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Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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Authors: Samai'la Abdullahi

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A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table.

Keywords: euler circuit and path, graph representation of circuit networks, representation of graph models, representation of circuit network using logical truth table

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Authors: Vadim E. Levit, Eugen Mandrescu

Abstract:

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

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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 223