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Journal articles on the topic 'Relations with graph theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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1

Weaver, Nik. "Quantum Graphs as Quantum Relations." Journal of Geometric Analysis 31, no. 9 (2021): 9090–112. http://dx.doi.org/10.1007/s12220-020-00578-w.

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AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Tr

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2

ILYUTKO, DENIS PETROVICH, and VASSILY OLEGOVICH MANTUROV. "INTRODUCTION TO GRAPH-LINK THEORY." Journal of Knot Theory and Its Ramifications 18, no. 06 (2009): 791–823. http://dx.doi.org/10.1142/s0218216509007191.

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The present paper is an introduction to a combinatorial theory arising as a natural generalization of classical and virtual knot theory. There is a way to encode links by a class of "realizable" graphs. When passing to generic graphs with the same equivalence relations we get "graph-links". On one hand graph-links generalize the notion of virtual link, on the other hand they do not detect link mutations. We define the Jones polynomial for graph-links and prove its invariance. We also prove some a generalization of the Kauffman–Murasugi–Thistlethwaite theorem on "minimal diagrams" for graph-lin

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Prabha, S. Celine, M. Palanivel, S. Amutha, et al. "Solutions of Detour Distance Graph Equations." Sensors 22, no. 21 (2022): 8440. http://dx.doi.org/10.3390/s22218440.

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Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.

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Aharwal, Ramesh Prasad. "Graph Theory Applications in Machine Learning." International Journal for Research in Applied Science and Engineering Technology 13, no. 3 (2025): 645–48. https://doi.org/10.22214/ijraset.2025.67337.

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Graph theory is the Branch of Discrete mathematics which plays a key role in Machine Learning and Data Science. Graph Theory in Machine Learning states to the application of mathematical structures known as graphs to model pairwise relations between objects in machine learning. A graph in this framework is a set of objects, called nodes, connected by links, known as edges. Each edge may be directed or undirected. In mathematics, graph theory is one of the important fields used in structural models. This paper explores the applications of Graph theory and various types of graphs in Machine Lear

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Yurttas Gunes, Aysun, Muge Togan, Musa Demirci, and Ismail Naci Cangul. "Harmonic Index and Zagreb Indices of Vertex-Semitotal Graphs." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1260–69. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3725.

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Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex-semitotal graphs are calculated. So

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Zhou, Chao, and Yan Ping Liu. "Study on Parameter Transfer Structure of Generalized Modular Based Graph Theory." Advanced Materials Research 562-564 (August 2012): 1323–26. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1323.

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For the purpose of reducing product structure levels and shorting transfer chain of parameter, in this paper the product structure levels are expressed with generalized modular. The concept of directed graph of parameter connection structure for generalized modular is proposed with the use of directed graph theory, generalized modular, sub-modular and part represented by vertex, the driven relations of parameter connection represented by directed edge, and the properties of directed graph of parameter connection structure for generalized modular are gained. The directed graph of parameter conn

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Javaid, Imran, Shahroz Ali, Shahid Ur Rehman, and Aqsa Shah. "Rough sets in graphs using similarity relations." AIMS Mathematics 7, no. 4 (2022): 5790–807. http://dx.doi.org/10.3934/math.2022320.

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<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $

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Hashemi, Ebrahim, Mona Abdi, Abdollah Alhevaz, and Huadong Su. "Domination number of graphs associated with rings." Journal of Algebra and Its Applications 19, no. 01 (2019): 2050009. http://dx.doi.org/10.1142/s0219498820500097.

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The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. Let [Formula: see text] be an associative (not necessarily commutative) ring. We focus on the domination number of the zero-divisor graph [Formula: see text], the compressed zero-divisor graph [Formula: see text] and the unit graph [Formula: see text]. We find some relations between the domination number of the zero-divisor graph and that of the compressed zero-divisor graph. Moreover, some relations between the domination number of [Formula: s

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9

SHENOY, PRAKASH P. "REPRESENTING CONDITIONAL INDEPENDENCE RELATIONS BY VALUATION NETWORKS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 02, no. 02 (1994): 143–65. http://dx.doi.org/10.1142/s0218488594000134.

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Valuation networks have been proposed as graphical representations of valuation-based systems. The axiomatic framework of valuation-based systems is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory, Spohn's epistemic belief theory, and Zadeh's possibility theory. In this paper, we show how valuation networks encode conditional independence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, directed acyclic graph models, directed balloon graph models

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De Bueriis, Giustino, and Alberto Maria Langella. "Algebraic Lexicon Grammar." International Journal of Linguistics 11, no. 3 (2019): 21. http://dx.doi.org/10.5296/ijl.v11i3.14766.

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This article aims at showing an application of graph theory to the description of the syntactic relations between words in English. Graph theory is part of Network Science, a new and compelling branch of mathematics that has undergone huge development over the past 20 years. The linguistic theoretical background is the Lexicon Grammar (LG) that in turn is built on the ground of the Harrisian grammar for operators and arguments. Graph theory is particularly useful in order to show how sentences have underlying structures that can be visualized through the use of graphs, and whose properties can

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Hee-kyung Moon, Chang-ho An, Zhanfang Zhao,. "Graph-Based Representation Of Syntactic Structures Of Natural Languages Based On Dependency Relations." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (2021): 293–301. http://dx.doi.org/10.17762/turcomat.v12i5.901.

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Deep Learning approach using probability distribution to natural language processing achieves significant accomplishment. However, natural languages have inherent linguistic structures rather than probabilistic distribution. This paper presents a new graph-based representation of syntactic structures called syntactic knowledge graph based on dependency relations. This paper investigates the valency theory and the markedness principle of natural languages to derive an appropriate set of dependency relations for the syntactic knowledge graph. A new set of dependency relations derived from the ma

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Hasegawa, Takehiro, and Seiken Saito. "A generalization of the graph theory prime-number theorem of a finite graph." International Journal of Mathematics 26, no. 09 (2015): 1550071. http://dx.doi.org/10.1142/s0129167x15500718.

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In the first half, we present a generalization of the graph theory prime-number theorem due to Audrey Terras et al. In the last half, we study relations between several densities of a subset consisting of primes in a graph, and by using the first result, we compute a distribution of a subset. This is an answer for the "research problem" in the page 197 of Terras' textbook "Zeta Functions of Graphs."

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Hanif, Muhammad Zeeshan, Naveed Yaqoob, Muhammad Riaz, and Muhammad Aslam. "Linear Diophantine fuzzy graphs with new decision-making approach." AIMS Mathematics 7, no. 8 (2022): 14532–56. http://dx.doi.org/10.3934/math.2022801.

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<abstract><p>The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these o

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Sun, Weiwei, Yufei Chen, Xiaojun Wan, and Meichun Liu. "Parsing Chinese Sentences with Grammatical Relations." Computational Linguistics 45, no. 1 (2019): 95–136. http://dx.doi.org/10.1162/coli_a_00343.

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We report our work on building linguistic resources and data-driven parsers in the grammatical relation (GR) analysis for Mandarin Chinese. Chinese, as an analytic language, encodes grammatical information in a highly configurational rather than morphological way. Accordingly, it is possible and reasonable to represent almost all grammatical relations as bilexical dependencies. In this work, we propose to represent grammatical information using general directed dependency graphs. Both only-local and rich long-distance dependencies are explicitly represented. To create high-quality annotations,

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15

SARKAR, Prosanta, Sourav MONDAL, Nilanjan DE, and Anita PAL. "(a,b)- Zagreb index of some special graph." Revue Roumaine de Chimie 65, no. 11 (2021): 1045–55. http://dx.doi.org/10.33224/rrch.2020.65.11.09.

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In the past few years, graph theory has emerged as one of the most powerful mathematical tools to model many types of relations and process dynamics in computer science, biological and social systems. Generally, a graph is depicted as a set of nodes which is called vertices connected by lines are called edges. A topological index is the numerical parameter of a graph that characterizes its topology and it is usually graph invariant. In this paper, we compute some important classes vertex degree-based graph invariants using the Zagreb index of some special graphs such as the co-normal product o

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Mitic, Vojislav V., Goran Lazovic, Branislav Randjelovic, et al. "Graph theory applied to microelectronics intergranular relations." Ferroelectrics 570, no. 1 (2021): 145–52. http://dx.doi.org/10.1080/00150193.2020.1839265.

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S.R.Ramachandra. "A STUDY ON GRAPH THEORY IN DISCRETE MATHEMATICS." Shanlax International Journal of Arts, Science and Humanities 6, S2 (2019): 249–57. https://doi.org/10.5281/zenodo.2651985.

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<em>Graph theory, the study of graphs and networks, is often considered part of combinatory, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational dev

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18

Taha H. Jasim and Aiad I. Awad. "Some Topological Concepts Via Graph Theory." Tikrit Journal of Pure Science 25, no. 4 (2020): 117–22. http://dx.doi.org/10.25130/tjps.v25i4.280.

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Due it is difficult to find applications in topological spaces, which are branches of pure mathematics, the importance of this paper is to find applications in graph theory. Via some concepts of topological space we generalizes to a graph like (graph interior, graph closure graph exterior, graph boundary, graph limit point). The relations among them were studied. At least many theorems were proofed as a characterization and some examples introduced to explain the subject

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19

Kechris, Alexander. "Global aspects of measure preserving equivalence relations and graphs." New Zealand Journal of Mathematics 52 (November 10, 2021): 691–726. http://dx.doi.org/10.53733/96.

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This paper is an introduction and survey of a “global” theory of measure preserving equivalence relations and graphs. In this theory one views a measure preserving equivalence relation or graph as a point in an appropriate topological space and then studies the properties of this space from a topological, descriptive set theoretic and dynamical point of view.

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20

Janz, Arkadiusz, Paweł Kędzia, and Maciej Piasecki. "Graph-Based Complex Representation in Inter-Sentence Relation Recognition in Polish Texts." Cybernetics and Information Technologies 18, no. 1 (2018): 152–70. http://dx.doi.org/10.2478/cait-2018-0013.

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Abstract This paper presents a supervised approach to the recognition of Cross-document Structure Theory (CST) relations in Polish texts. Its core is a graph-based representation constructed for sentences. Graphs are built on the basis of lexicalised syntactic-semantic relations extracted from text. Similarity between sentences is calculated as similarity between their graphs, and the values are used as features to train the classifiers. Several different configurations of graphs, as well as graph similarity methods were analysed for this task. The approach was evaluated on a large open corpus

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21

Shi, Haizhong, and Yue Shi. "Random graph languages." Discrete Mathematics, Algorithms and Applications 09, no. 02 (2017): 1750020. http://dx.doi.org/10.1142/s1793830917500203.

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There tend to be no related researches regarding the relationships between graph theory and languages ever since the concept of graph-semigroup was first proposed in 1991. In 2011, after finding out the inner co-relations among digraphs, undirected graphs and languages, we proposed certain concepts including undirected graph language and digraph language; moreover, in 2014, we proposed a broaden concept–(V,R)-language and proved: (1) both undirected graph language and digraph language are (V,R)-languages; (2) both undirected graph language and digraph language are regular languages; (3) natura

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22

Лобас, Е. Р., Д. Канфора, С. Г. Руднев, and К. А. Ковалева. "Corruption analysis through mathematical methods of graph theory." Applied Economic Researches Journal, no. 1 (March 30, 2024): 45–52. http://dx.doi.org/10.47576/2949-1908.2024.1.1.005.

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Статья посвящена применению графовой теории в моделировании коррупционных схем. Графовая теория предоставляет ценные инструменты для анализа сложных взаимосвязей между участниками коррупционных действий. Исследование направлено на изучение потенциала данной теории для выявления и анализа структуры и динамики коррупционных отношений. Предлагается методология построения графов коррупционных сетей и анализа их характеристик, что позволяет углубить понимание механизмов функционирования и распространения коррупции в социально-экономических и политических системах. The article is devoted to the appl

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Flippen, Christopher, Allison H. Moore, and Essak Seddiq. "Quotients of the Gordian and H(2)-Gordian graphs." Journal of Knot Theory and Its Ramifications 30, no. 05 (2021): 2150037. http://dx.doi.org/10.1142/s0218216521500371.

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The Gordian graph and H(2)-Gordian graphs of knots are abstract graphs whose vertex sets represent isotopy classes of unoriented knots, and whose edge sets record whether pairs of knots are related by crossing changes or H(2)-moves, respectively. We investigate quotients of these graphs under equivalence relations defined by several knot invariants including the determinant, the span of the Jones polynomial, and an invariant related to tricolorability. We show, in all cases considered, that the quotient graphs are Gromov hyperbolic. We then prove a collection of results about the graph isomorp

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Et. al., Peruri Lakshmi Narayana Varma ,. "Study of Circular Distance in Graphs." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (2021): 2437–44. http://dx.doi.org/10.17762/turcomat.v12i2.2067.

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Circular distance between vertices of a graph has a significant role, which is defined as summation of detour distance and geodesic distance. Attention is paid, this is metric on the set of all vertices of graph and it plays an important role in graph theory. Some bounds have been carried out for circular distance in terms of pendent vertices of graph . Some results and properties have been found for circular distance for some classes of graphs and applied this distance to Cartesian product of graphs〖 P〗_2×C_n. Including 〖 P〗_2×C_n, some graphs acted as a circular self-centered. Using this cir

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AL-TAHAN, MADELEINE, and BIJAN DAVVAZ. "Hypergroups Defined on Hypergraphs and their Regular Relations." Kragujevac Journal of Mathematics 46, no. 3 (2022): 487–98. http://dx.doi.org/10.46793/kgjmat2203.487t.

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The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory. In this paper, we present some connections between hypergraph theory and hypergroup theory. In this regard, we construct two hypergroupoids by deﬁning two new hyperoperations on ℍ, the set of all hypergraphs. We prove that our deﬁned hypergroupoids are commutative hypergroups and we deﬁne hyperrings on ℍ by using the two deﬁned hyperoperations. Moreover, we study the fundamental group, complete parts, automorphism group a

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Filippova, P. A. "Values of the weight system on a family of graphs that are not the intersection graphs of chord diagrams." Sbornik: Mathematics 213, no. 2 (2022): 235–67. http://dx.doi.org/10.1070/sm9519.

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Abstract The Chmutov-Lando theorem claims that the value of a weight system (a function on the chord diagrams that satisfies the four-term Vassiliev relations) corresponding to the Lie algebra depends only on the intersection graph of the chord diagram. We compute the values of the weight system at the graphs in several infinite series, which are the joins of a graph with a small number of vertices and a discrete graph. In particular, we calculate these values for a series in which the initial graph is the cycle on five vertices; the graphs in this series, apart from the initial one, are not i

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Sun, Qingyun, Jianxin Li, Hao Peng, et al. "Graph Structure Learning with Variational Information Bottleneck." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 4165–74. http://dx.doi.org/10.1609/aaai.v36i4.20335.

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Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real-world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL is the first atte

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Qiao, Sha, Ping Zhu, and Witold Pedrycz. "Rough set analysis of graphs." Filomat 36, no. 10 (2022): 3331–54. http://dx.doi.org/10.2298/fil2210331q.

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Relational data has become increasingly important in decision analysis in recent years, and so mining knowledge which preserves relationships between objects is an important topic. Graphs can represent the knowledge which contains objects and relationships between objects. Rough set theory provides an effective tool for extracting knowledge, but it is not sufficient to extract the knowledge containing the data on relationships between objects. In order to extend the application scope and enrich the rough set theory, it is essential to develop a rough set analysis of graphs. This extension is i

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Moser, Louise E. "Decidability of Formulas in Graph Theory." Fundamenta Informaticae 12, no. 2 (1989): 163–80. http://dx.doi.org/10.3233/fi-1989-12204.

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A decision procedure is given for determining the validity of unquantified formulas in graph theory. The procedure, which decides equality and containment relations for vertex, edge, and graph terms, reduces to a decision procedure for propositional calculus. The correctness of the procedure is proved using model theory based on the axioms for graph theory provided. The complexity of the algorithm and its limitations are discussed.

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CONLEY, CLINTON T., ALEXANDER S. KECHRIS, and ROBIN D. TUCKER-DROB. "Ultraproducts of measure preserving actions and graph combinatorics." Ergodic Theory and Dynamical Systems 33, no. 2 (2012): 334–74. http://dx.doi.org/10.1017/s0143385711001143.

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AbstractUltraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.

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Mitic, Vojislav V., Branislav Randjelovic, Ivana Ilic, et al. "The 3D graph approach for breakdown voltage calculation in BaTiO3 ceramics." International Journal of Modern Physics B 35, no. 07 (2021): 2150103. http://dx.doi.org/10.1142/s0217979221501034.

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After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various cryst

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LOVÁSZ, LÁSZLÓ, and KATALIN VESZTERGOMBI. "Non-Deterministic Graph Property Testing." Combinatorics, Probability and Computing 22, no. 5 (2013): 749–62. http://dx.doi.org/10.1017/s0963548313000205.

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A property of finite graphs is called non-deterministically testable if it has a ‘certificate’ such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that non-deterministically testable properties are also deterministically testable.

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Kalampakas, Antonios. "Graph Automata and Graph Colorability." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 112–20. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4629.

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Automata recognizing graphs can be constructed by employing the algebraic structure of graphoids. For the construction of a graph automaton, the relations over the Kleene star of the state set must constitute a graphoid. Hence different kinds of graphoids produce graph automata with diverse operation and recognition capacity. In this paper we show that graph colorability is recognized by automata operating over the simplest possible abelian graphoid.

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Bilar, Vergel, Maria Andrea Bonsocan, Javier Hassan, and Susan Dagondon. "Vertex Cover Hop Dominating Sets in Graphs." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 93–104. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.4978.

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Let $G$ be a graph. Then a subset $C$ of vertices of $G$ is called a vertex cover hop dominating if $C$ is both a vertex cover and a hop dominating of $G$. The vertex cover hop domination number of $G$, denoted by $\gamma_{vch}(G)$, is the minimum cardinality among all vertex cover hop dominating sets in $G$. In this paper, we initiate the study of vertex cover hop domination in a graph and we determine its relations with other parameters in graph theory. We characterize the vertex cover hop dominating sets in some special graphs, join, and corona of two graphs and we finally obtain the exact

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Fatima Ibrahim Fathi, Nabeel Ezzulddin Arif, and Luma Saad Abdalbaqi. "Some Result on Supra Separation Axioms via Graph Theory." Tikrit Journal of Pure Science 27, no. 1 (2022): 115–21. http://dx.doi.org/10.25130/tjps.v27i1.88.

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The Concepts of supra topological graph and introduces of class supra separation axioms on supra topological graph (supra gT0, supra gT1,supra gT2,supra gT3,supra gT4), many relations among them were studied. Gave results for them.

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Susilowati, Liliek, Utik Maulida, Nenik Estuningsih, Siti Zahidah, and Savari Prabhu. "On the central resolver set of the edge coronation graphs." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 1 (2025): 29–42. https://doi.org/10.47974/jdmsc-1819.

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Graph theory as part of mathematics, has experienced significant development from the theoretical aspect, one of it is the theory of metric dimension. The concept of metric dimensions has evolved greatly, including the dominant metric dimension and the complement metric dimension. In this study, the concept of the central metric dimension is introduced, that is a combination of the metric dimension and central of a graph. The minimum number of vertices of a resolver set that contains a central set is called the central metric dimension of graph G, and denoted by dimcen(G). Several characteriza

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Dutta, Supriyo, Bibhas Adhikari, and Subhashish Banerjee. "Condition for zero and nonzero discord in graph Laplacian quantum states." International Journal of Quantum Information 17, no. 02 (2019): 1950018. http://dx.doi.org/10.1142/s0219749919500187.

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This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corres

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Li, Shu, and Jianfeng Wang. "Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs." Algebra Colloquium 30, no. 03 (2023): 493–502. http://dx.doi.org/10.1142/s1005386723000408.

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A signed graph [Formula: see text] is a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], together with a function [Formula: see text] assigning a positive or negative sign to each edge. In this paper, we present a more elementary proof for the matrix-tree theorem of signed graphs, which is based on the relations between the incidence matrices and the Laplcians of signed graphs. As an application, we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.

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Yegnanarayanan, VENKATRAMAN, NARAYANAA Y. Krithicaa, E. BALAS Valentina, and RAD Dana. "Graph Theory Applications to Comprehend Epidemics Spread of a Disease." BRAIN. Broad Research in Artificial Intelligence and Neuroscience 12, no. 2 (2025): 161–77. https://doi.org/10.18662/brain/12.2/198.

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 Theory of Graphs could offer a plenty to enrich the analysis and modelling to generate datasets out of the systems and processes regarding the spread of a disease that affects humans, animals, plants, crops etc., In this paper first we show graphs can serve as a model for cattle movements from one farm to another. Second, we give a crisp explanation regarding disease transmission models on contact graphs/networks. It is possible to indicate how a regular tree exhibits relations among graph structure and the infectious disease spread and how certain

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Das, Kinkar Chandra, Ahmet Sinan Çevik, Ismail Naci Cangul, and Yilun Shang. "On Sombor Index." Symmetry 13, no. 1 (2021): 140. http://dx.doi.org/10.3390/sym13010140.

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The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

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Olifer, Dmitrij, Nikolaj Goranin, Antanas Cenys, Arnas Kaceniauskas, and Justinas Janulevicius. "Defining the Minimum Security Baseline in a Multiple Security Standards Environment by Graph Theory Techniques." Applied Sciences 9, no. 4 (2019): 681. http://dx.doi.org/10.3390/app9040681.

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One of the best ways to protect an organization’s assets is to implement security requirements defined by different standards or best practices. However, such an approach is complicated and requires specific skills and knowledge. In case an organization applies multiple security standards, several problems can arise related to overlapping or conflicting security requirements, increased expenses on security requirement implementation, and convenience of security requirement monitoring. To solve these issues, we propose using graph theory techniques. Graphs allow the presentation of security req

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Nazary, Abdul Jamil, and Gulistan Zarifi. "Role of Rectangular and Square Matrix in Graph Theory." International Journal of Social Science Research and Review 7, no. 12 (2025): 179–91. https://doi.org/10.47814/ijssrr.v7i12.2441.

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Graph theory is one of the topics studied in modern mathematics and the concept of graph in mathematics was discussed from the past to the present. For example, graph relations and functions have many uses. The 18th century is the beginning of modern graph theory. From the 19th century onwards, graph theory was discussed for its application in various fields, which is a field of research at this time. Graph theory and matrix are two important and well-known topics in modern mathematics, so in this article the role of rectangular and square matrix in graph theory is discussed. The main purpose

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Shiono, Yasunori, Tadaaki Kirishima, Yoshinori Ueda, and Kensei Tsuchida. "Drawing Algorithm for Fuzzy Graphs Using the Partition Tree." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 5 (2012): 641–52. http://dx.doi.org/10.20965/jaciii.2012.p0641.

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Fuzzy graphs have been used frequently and effectively as a method for sociogram analysis. A fuzzy graph has the fundamental characteristic of being able to express a variety of relationships between nodes. The drawing of fuzzy graphs has been studied in computer-aided analysis systems with human interfaces and methods using genetic algorithms. However, computer-aided analysis systems with human interfaces do not provide for automatic drawing, while methods using genetic algorithms have the defect of requiring too much execution time for finding a locally optimum solution. To overcome these de

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Mitic, Vojislav, Branislav Randjelovic, Srdjan Ribar, et al. "Thermal parameters defined with graph theory approach in synthetized diamonds." Thermal Science, no. 00 (2021): 284. http://dx.doi.org/10.2298/tsci210422284m.

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The Nanocrystaline diamonds are very important biomedical material with variety of applications. The experimental procedures and results have been done in the Institute of Functional Nanosystems at the University Ulm (Germany). There is an existing biocompatibility of the diamond layers, selectively improved by biomimetic 3D patterns structuring. Based on that, we have been inspired to apply the graph theory approach in analysing and defining the physical parameters within the structure of materials structure samples. Instead the parameters values, characteristic at the samples surface, we pen

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B. K. Divyashree, Jagadeesh R, and Siddabasappa. "The M-polynomials of some Chemical Graphs." RESEARCH REVIEW International Journal of Multidisciplinary 7, no. 1 (2022): 86–99. http://dx.doi.org/10.31305/rrijm.2022.v07.i01.012.

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The chemical graph theory (CGT)is one of the branches in mathematical chemistry. It is utilized to address the number of problems related to molecular theory which has its utilization in graph theory as an application. The CGT reduces the structure of the molecule to a single value which is used to mark either to its structural fragments, orbital’s, the molecular branching, energy of the molecule as a whole, its electronic structures and many other properties by using these invariants. These invariants estimate the relations of physical evident estimations by performing experiments in a way th

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Wasilewski, Mateusz. "On quantum Cayley graphs." Documenta Mathematica 29, no. 6 (2024): 1281–317. http://dx.doi.org/10.4171/dm/987.

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We clarify the correspondence between two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side and suggest an extension of the theory of quantum graphs to the infinite dimensional case. Then we use this framework to introduce quantum graphs associated to discrete quantum groups, leading to a new definition of a quantum Cayley graph.

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Filipovski, Slobodan. "Relations between the energy of graphs and other graph parameters." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 3 (2021): 661–72. http://dx.doi.org/10.46793/match.87-3.661f.

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In this paper we give various relations between the energy of graphs and other graph parameters as Randić index, clique number, number of vertices and edges, maximum and minimum degree etc. Moreover, new bounds for the energy of complementary graphs are derived. Our results are based on the concept of vertex energy developed by G. Arizmendi and O. Arizmendi in [Lin. Algebra Appl. doi:10.1016/j.laa.2020.09.025].

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Vitkauskas, Jonas, and Artūras Štikonas. "Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theory." Lietuvos matematikos rinkinys 61 (February 18, 2021): 1–6. http://dx.doi.org/10.15388/lmr.2020.22474.

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Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of spectrum curves. In this paper, relations between discrete Sturm-Liouville problem with nonlocal boundary conditions characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found.

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Tsvetov, V. P. "Algebras of finitary relations." Information Technology and Nanotechnology, no. 2416 (2019): 119–25. http://dx.doi.org/10.18287/1613-0073-2019-2416-119-125.

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Algebras of finitary relations naturally generalize the algebra of binary relations with the left composition. In this paper, we consider some properties of such algebras. It is well known that we can study the hypergraphs as finitary relations. In this way the results can be applied to graph and hypergraph theory, automatons and artificial intelligence.

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Wang, Yajing, and Yubin Gao. "Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy." Mathematical Problems in Engineering 2020 (July 16, 2020): 1–7. http://dx.doi.org/10.1155/2020/5898735.

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Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new

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