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Journal articles on the topic 'Graph theary'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Kakali, Datta. "Eigenspectral features of some radialene-related conjugated systems." Journal of Indian Chemical Society 93, Jun 2016 (2016): 635–38. https://doi.org/10.5281/zenodo.5638602.

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M. U. C. Women’s College, B. C. Road, Burdwan-713 104, West Bengal, India <em>E-mail </em>: dnkakali@rediffmail.com <em>Manuscript received 15 March 2016, accepted 03 May 2016</em> л-MO energies of some radialenes (Rn) and radialene-derived quinonoids (R<sub>n</sub><sup>Q)</sup> at the Hückel level have been determined graph theoretically. Strong subspectrality is shown to exist among the graph eigenspectra (i.e. the set of HMO energy eigenvalues) and the origin of such subspectrality has been shown to be rooted in rotational symmetry which results in circulant nature of the adjacen

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CSIKVÁRI, PÉTER, and ZOLTÁN LÓRÁNT NAGY. "The Density Turán Problem." Combinatorics, Probability and Computing 21, no. 4 (2012): 531–53. http://dx.doi.org/10.1017/s0963548312000016.

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LetHbe a graph onnvertices and let the blow-up graphG[H] be defined as follows. We replace each vertexviofHby a clusterAiand connect some pairs of vertices ofAiandAjif (vi,vj) is an edge of the graphH. As usual, we define the edge density betweenAiandAjasWe study the following problem. Given densities γijfor each edge (i,j) ∈E(H), one has to decide whether there exists a blow-up graphG[H], with edge densities at least γij, such that one cannot choose a vertex from each cluster, so that the obtained graph is isomorphic toH,i.e., noHappears as a transversal inG[H]. We calldcrit(H) the maximal va

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Fujita, Takaaki. "Claw-free Graph and AT-free Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs." Information Sciences with Applications 5 (March 5, 2025): 40–55. https://doi.org/10.61356/j.iswa.2025.5502.

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Graph theory studies networks consisting of nodes (vertices) and their connections (edges), with various graph classes being extensively researched. This paper focuses on three specific graph classes: AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs. Additionally, it examines uncertain graph models, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, which are designed to address uncertainty in diverse applications. In this study, we introduce and analyze AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs within the framework of Fuzzy Graphs, investig

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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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Prajapati, Rajeshri, Amit Parikh, and Pradeep Jha. "Exploring Novel Edge Connectivity in Graph Theory and its Impact on Eulerian Line Graphs." International Journal of Science and Research (IJSR) 12, no. 11 (2023): 1515–19. http://dx.doi.org/10.21275/sr231120155230.

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Pardo-Guerra, Sebastian, Vivek Kurien George, Vikash Morar, Joshua Roldan, and Gabriel Alex Silva. "Extending Undirected Graph Techniques to Directed Graphs via Category Theory." Mathematics 12, no. 9 (2024): 1357. http://dx.doi.org/10.3390/math12091357.

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We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘prime graphs category’; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs

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JOHANNSEN, DANIEL, MICHAEL KRIVELEVICH, and WOJCIECH SAMOTIJ. "Expanders Are Universal for the Class of All Spanning Trees." Combinatorics, Probability and Computing 22, no. 2 (2013): 253–81. http://dx.doi.org/10.1017/s0963548312000533.

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A graph is calleduniversalfor a given graph class(or, equivalently,-universal) if it contains a copy of every graph inas a subgraph. The construction of sparse universal graphs for various classeshas received a considerable amount of attention. There is particular interest in tight-universal graphs, that is, graphs whose number of vertices is equal to the largest number of vertices in a graph from. Arguably, the most studied case is that whenis some class of trees. In this work, we are interested in(n,Δ), the class of alln-vertex trees with maximum degree at most Δ. We show that everyn-vertex

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Fujita, Takaaki. "Review of Rough Turiyam Neutrosophic Directed Graphs and Rough Pentapartitioned Neutrosophic Directed Graphs." Neutrosophic Optimization and Intelligent Systems 5 (March 4, 2025): 48–79. https://doi.org/10.61356/j.nois.2025.5500.

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Graph theory, a fundamental branch of mathematics, examines relationships between entities through the use of vertices and edges. Within this field, Uncertain Graph Theory has developed as a powerful framework to represent the uncertainties found in real world networks. Among the various uncertain graph models, Turiyam Neutrosophic Graphs and Pentapartitioned Neutrosophic Graphs are well-established. However, their extension to Directed Graphs remains relatively unexplored. To address this gap, this paper presents the concepts of the Turiyam Neutrosophic Directed Graph and the Pentapartitioned

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Cvetkovic, Dragos, and Slobodan Simic. "Towards a spectral theory of graphs based on the signless Laplacian, I." Publications de l'Institut Math?matique (Belgrade) 85, no. 99 (2009): 19–33. http://dx.doi.org/10.2298/pim0999019c.

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A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies

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Möhring, Rolf H. "Algorithmic graph theory and perfect graphs." Order 3, no. 2 (1986): 207–8. http://dx.doi.org/10.1007/bf00390110.

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A. Antony mary, A., A. Amutha, and M. S. Franklin Thamil Selvi. "A Study on Slope Number of Certain Classes of Bipartite Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 440. http://dx.doi.org/10.14419/ijet.v7i4.10.21036.

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Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs crea

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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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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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Firmansah, Fery, and Wed Giyarti. "Odd harmonious labeling on the amalgamation of the generalized double quadrilateral windmill graph." Desimal: Jurnal Matematika 4, no. 3 (2021): 373–78. http://dx.doi.org/10.24042/djm.v4i3.10823.

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Graph labeling is one of the topics of graph theory that is growing very rapidly both in terms of theory and application. A graph that satisfies the labeling property of odd harmonious is called an odd harmonious graph. The method used in this research is qualitative research by developing a theory and a new class of graphs from odd harmonious graphs. In this research, a new graph class construction will be given in the form of an amalgamation of the generalized double quadrilateral windmill graph. Furthermore, it will be proved that the amalgamation of the generalized double quadrilateral win

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Redmon, Eric, Miles Mena, Megan Vesta, et al. "Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA." PUMP Journal of Undergraduate Research 6 (March 13, 2023): 124–50. http://dx.doi.org/10.46787/pump.v6i0.2427.

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Motivated by the recent advancements in nanotechnology and the discovery of new laboratory techniques using the Watson-Crick complementary properties of DNA strands, formal graph theory has recently become useful in the study of self-assembling DNA complexes. Construction methods based on graph theory have resulted in significantly increased efficiency. We present the results of applying graph theoretical and linear algebra techniques for constructing crossed-prism graphs, crown graphs, book graphs, stacked book graphs, and helm graphs, along with kite, cricket, and moth graphs. In particular,

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Seema Varghese and Brinta Babu. "An overview on graph products." International Journal of Science and Research Archive 10, no. 1 (2023): 966–71. http://dx.doi.org/10.30574/ijsra.2023.10.1.0848.

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Graph product is a very basic idea in graph theory. Graph products include a wide range of operations that join two or more existing graphs to produce new graphs with distinctive properties and uses. In this paper, we explore four forms of graph products, their characteristics, and their significance within the broader framework of graph theory.

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V.R.Kulli. "NEW DIRECTION IN THE THEORY OF GRAPH INDEX IN GRAPHS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 11, no. 12 (2023): 1–8. https://doi.org/10.5281/zenodo.7505790.

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Since 1972, several graph indices were introduced and studied. In this paper, we define the Banhatti degree of vertex in a graph. We propose the first and second E-Banhatti indices of a graph. A study of E-Banhatti indices in Mathematical Chemistry is a New Direction in the Theory of Graph Index in Graphs. Also we compute these newly defined E-Banhatti indices and their corresponding exponentials for wheel graphs, friendship graphs and some important nanostructures which are appeared in nanoscience.

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Pasupuleti, Murali Krishna. "Graph-Theoretical Intelligence for Adaptive Cybersecurity: Multi-Modal Models, Dynamic Defense, and Federated Threat Detection." International Journal of Academic and Industrial Research Innovations(IJAIRI) 05, no. 04 (2025): 347–56. https://doi.org/10.62311/nesx/rp3125.

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Abstract: The rise of sophisticated cyber threats demands adaptive, resilient, and intelligent cybersecurity mechanisms. Graph theory has emerged as a foundational tool for modeling, detecting, and responding to complex attack patterns. This paper critically interprets recent advancements across cybersecurity knowledge graphs, graph neural networks, attack graphs, and federated graph learning. A multi-modal, graph-theoretical intelligence framework is proposed to enhance dynamic defense and collaborative threat detection while maintaining privacy. Statistical analysis, visual models, and new s

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Tola, Keneni Abera, V. N. Srinivasa Rao Repalle, and Mamo Abebe Ashebo. "Theory and Application of Interval-Valued Neutrosophic Line Graphs." Journal of Mathematics 2024 (March 19, 2024): 1–17. http://dx.doi.org/10.1155/2024/5692756.

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Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is

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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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Saenpholphat, Varaporn, and Ping Zhang. "Conditional resolvability in graphs: a survey." International Journal of Mathematics and Mathematical Sciences 2004, no. 38 (2004): 1997–2017. http://dx.doi.org/10.1155/s0161171204311403.

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For an ordered setW={w1,w2,…,wk}of vertices and a vertexvin a connected graphG, the code ofvwith respect toWis thek-vectorcW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), whered(x,y)represents the distance between the verticesxandy. The setWis a resolving set forGif distinct vertices ofGhave distinct codes with respect toW. The minimum cardinality of a resolving set forGis its dimensiondim(G). Many resolving parameters are formed by extending resolving sets to different subjects in graph theory, such as the partition of the vertex set, decomposition and coloring in graphs, or by combining resolving property

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Nada A Laabi. "Subring in Graph Theory." Advances in Nonlinear Variational Inequalities 27, no. 4 (2024): 284–87. http://dx.doi.org/10.52783/anvi.v27.1526.

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In our study, we delved into the intricacies of graph theory by exploring the properties of subrings within various types of graphs. By focusing on prime graphs and simple graphs, we unraveled the complex relationship between subring-prime graphs. Additionally, we delved into the concept of homomorphism within both simple subring graphs and prime subring graphs, adding depth to our analysis.

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Ali, Muhammad Asad, Muhammad Shoaib Sardar, Imran Siddique, and Dalal Alrowaili. "Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph." Journal of Chemistry 2021 (October 26, 2021): 1–12. http://dx.doi.org/10.1155/2021/7057412.

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A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double gra

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Pradeep Jha, Rajeshri Prajapati, Amit Parikh,. "Special Graphs of Euler’s Family* and Tracing Algorithm- (A New Approach)." Proceeding International Conference on Science and Engineering 11, no. 1 (2023): 2243–51. http://dx.doi.org/10.52783/cienceng.v11i1.400.

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There are in graph theory, some known graphs which date back from centuries. [Euler graph, Hamiltonian graph etc.] These graphs are basic roots for development of graph theory. In this paper we have discussed the novel concept of tracing Euler tour. It depends on the concept of Link vertex - a join vertex of finite number of cycles as components of Euler graph. In addition to this, a new notion of isomorphic transformation of given graph on to a given line segment known as ‘Linear Graph’ also plays an important role for tracing the Euler graph.

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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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Fujita, Takaaki. "Permutation Graphs in Fuzzy and Neutrosophic Graphs." Multicriteria Algorithms with Applications 7 (April 2, 2025): 1–18. https://doi.org/10.61356/j.mawa.2025.7523.

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Graph theory is a fundamental branch of mathematics that examines networks composed of nodes (vertices) and connections (edges). This paper explores the concepts of permutation graphs within the frameworks of fuzzy, intuitionistic fuzzy, neutrosophic, and Turiyam Neutrosophic graphs, all of which handle uncertainty in graph structures. We define permutation and bipartite permutation graphs in each context and investigate their properties. While permutation graphs have been studied extensively in classical graph theory, there has been limited exploration in fuzzy and neutrosophic settings.

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KIYOMI, MASASHI, TOSHIKI SAITOH, and RYUHEI UEHARA. "BIPARTITE PERMUTATION GRAPHS ARE RECONSTRUCTIBLE." Discrete Mathematics, Algorithms and Applications 04, no. 03 (2012): 1250039. http://dx.doi.org/10.1142/s1793830912500395.

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The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

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Kitaev, Sergey, and Haoran Sun. "Human-verifiable proofs in the theory of word-representable graphs." RAIRO - Theoretical Informatics and Applications 58 (2024): 9. http://dx.doi.org/10.1051/ita/2024004.

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A graph is word-representable if it can be represented in a certain way using alternation of letters in words. Word-representable graphs generalise several important and well-studied classes of graphs, and they can be characterised by semi-transitive orientations. Recognising word-representability is an NP-complete problem, and the bottleneck of the theory of word-representable graphs is convincing someone that a graph is non-word-representable, keeping in mind that references to (even publicly available and user-friendly) software are not always welcome. (Word-representability can be justifie

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Saleem, H., M. N. Husin, S. Ali, and M. S. Hameed. "On Examining Metric Dimension Through Edge Contraction in Certain Families of Graphs." Malaysian Journal of Mathematical Sciences 19, no. 2 (2025): 613–35. https://doi.org/10.47836/mjms.19.2.13.

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In graph theory, the Metric Dimension (MD) is an elementary metric that affords evidence nearly the essential selves of graphs. We reconnoiter the MD in the venue of edge-contracted regular graphs in this paper, with exceptional devotion to the Antiprism, Petersen, and Harary graphs. Our effort creates a vital bond between antiprism and its edge-contracted counterpart: we give a scheme to regulate the MD of the edge-contracted graph, given the MD of the novel graph. We likewise inspect how edge contraction affects regular graphs’ MDs, providing insight into how this operation deviations both t

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Vidyashree H. R. "Some Derived Graphs of Ananta-Graphs." Panamerican Mathematical Journal 35, no. 3s (2025): 522–27. https://doi.org/10.52783/pmj.v35.i3s.4246.

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Graph theory provides powerful tools for analyzing mathematical structures and sequences. The Ananta-graph, derived from the Collatz conjecture, represents integer transformations through directed edges, capturing number relationships under n→3n+1 and n→n/2 operations. This paper explores several derived graphs from the Ananta-graph, including line, middle, Mycielskian, subdivision, total, core, power, splitting and kernel graph, analyzing their structural properties and mathematical significance. By analyzing these derived graphs, we provide deeper insights into the topological, algebraic and

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Nagarajan, S., and B. Aswini. "The Minimum Reduced Sombor Index of Unicyclic Graphs in Terms of the Girth." Asian Research Journal of Mathematics 21, no. 2 (2025): 48–54. https://doi.org/10.9734/arjom/2025/v21i2892.

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Aims: The paper investigates the Reduced Sombor Index () for unicyclic graphs. Specifically, it aims to determine and characterize the unicyclic graphs that attain the minimum index among all unicyclic graphs of a given order. Study Design: This is a theoretical mathematical study based on graph theory and topological indices. The study involves defining and analyzing the Reduced Sombor Index by comparing values across different unicyclic graphs. Lemmas and theorems are proved to establish the minimum index graph. Methodology: Several graph transformation operations are analyzed. The study pro

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MACKIE, IAN, and DETLEF PLUMP. "Theory and applications of term graph rewriting: introduction." Mathematical Structures in Computer Science 17, no. 3 (2007): 361–62. http://dx.doi.org/10.1017/s0960129507006081.

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Term graph rewriting is concerned with the representation of functional expressions as graphs and the evaluation of these expressions by rule-based graph transformation. The advantage of computing with graphs rather than terms is that common subexpressions can be shared, improving the efficiency of computations in space and time. Sharing is ubiquitous in implementations of programming languages: many functional, logic, object-oriented and concurrent calculi are implemented using term graphs.

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Wafiq, Hibi. "Non-Isomorphism Between Graph And Its Complement." Multicultural Education 7, no. 6 (2021): 256. https://doi.org/10.5281/zenodo.4965942.

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<em>It is known that any graph with six vertices cannot be isomorphic to its complement [3].V. K. Balakrishnan has written in his book Schaum’s solved problems series [1] the following: “Given two arbitrary Simple graphs of the same order and the same size, the problem of determining whetheran isomorphism exists between the two is known as the isomorphism problem in graph theory. In general, itis not all easy (in other words, there is no "efficient algorithm") to solve an arbitrary instance of the isomorphismproblem”, from here came the idea of this paper. As mentio

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Solomko, Viktoriia, and Vladyslav Sobolev. "Constructing the Mate of Cospectral 5-regular Graphs with and without a Perfect Matching." Mohyla Mathematical Journal 4 (May 19, 2022): 24–27. http://dx.doi.org/10.18523/2617-70804202124-27.

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The problem of finding a perfect matching in an arbitrary simple graph is well known and popular in graph theory. It is used in various fields, such as chemistry, combinatorics, game theory etc. The matching of M in a simple graph G is a set of pairwise nonadjacent edges, ie, those that do not have common vertices. Matching is called perfect if it covers all vertices of the graph, ie each of the vertices of the graph is incidental to exactly one of the edges. By Koenig's theorem, regular bipartite graphs of positive degree always have perfect matching. However, graphs that are not bipartite ne

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Li, Rao. "The first Zagreb index conditions for Hamiltonian and traceable graphs." Open Journal of Discrete Applied Mathematics 8, no. 2 (2025): 45–51. https://doi.org/10.30538/psrp-odam2025.0115.

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The first Zagreb index of a graph is one of the most important topological indices in chemical graph theory. It is also an important invariant of general graphs. The first Zagreb index of a graph is defined as the sum of the squares of the degrees of the vertices in the graph. The research on the Hamiltonian properties of a graph is an important topic in graph theory. Use the Diaz-Metcalf inequality, we in this paper present new sufficient conditions based on the first Zagreb index for the Hamiltonian and traceable graphs. In addition, using the ideas of obtaining the sufficient conditions, we

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Fujita, Takaaki, and Florentin Smarandache. "A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs." Neutrosophic Systems with Applications 25, no. 2 (2025): 39–79. https://doi.org/10.61356/j.nswa.2025.25481.

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One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [84, 9, 135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs

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Akram, Muhammad, Wieslaw A. Dudek, and M. Murtaza Yousaf. "Regularity in Vague Intersection Graphs and Vague Line Graphs." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/525389.

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Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.

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K, SIVARANJANI, and Shanmuga Sundaram Olappalyam Vaiyapuri. "AN ANALYSIS OF THE SEIDEL LAPLACIAN ENERGY OF A FUZZY INTUITIONISTIC SYSTEM." Suranaree Journal of Science and Technology 32, no. 1 (2025): 0010350(1–14). https://doi.org/10.55766/sujst7197.

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This paper presents one of the latest research works in intuitionistic fuzzy graph theory. Along with questionable concepts conveyed in distinctive languages, intuitionistic fuzzy set theory offers a noteworthy and ground-breaking depiction of vulnerability estimation. The concept of energy is related to the spectrum of a graph. The energy of graphs plays a vital role in graph theory. In mathematics, the total sum of the absolute values of the eigenvalues of the graph’s adjacency matrix is referred to as the graph’s energy. In the framework of spectral graph theory, this quantity is extensivel

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Hosamani, S. M., V. B. Awati, and R. M. Honmore. "On graphs with equal dominating and c-dominating energy." Applied Mathematics and Nonlinear Sciences 4, no. 2 (2019): 503–12. http://dx.doi.org/10.2478/amns.2019.2.00047.

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AbstractGraph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

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Thenge, J. D., B. Surendranath Reddy, and Rupali S. Jain. "Contribution to Soft Graph and Soft Tree." New Mathematics and Natural Computation 15, no. 01 (2018): 129–43. http://dx.doi.org/10.1142/s179300571950008x.

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Soft set theory introduced by D. Molodstov is a new theory which deals with uncertainty. Connected graphs can be represented by using soft sets called soft graphs. In the present paper, we introduce the tabular representation of soft graph and define radius, diameter, center and degree of soft graph. We also define union, product of soft graphs and soft trees. We then derive some properties of radius, degree of vertex in soft graph and soft trees.

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Havare, Özge Çolakoğlu. "On Thorny Fuzzy Graphs." International Journal of Fuzzy Mathematical Archive 13, no. 02 (2017): 213–17. http://dx.doi.org/10.22457/ijfma.v13n2a11.

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A thorny fuzzy graph which is analogous to the concept thorny graphs in crisp graph theory is defined. The degree of an edge in thorny fuzzy graphs is obtained. Also, the degree of an edge in fuzzy graph formed by this operation in terms of the degree of edges in the given fuzzy graphs in some particular cases is found. Moreover, it is proved that thorny fuzzy graph of effective fuzzy graph is effective.

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Et. al., C. S. Harisha,. "Factorisation and Labeling in Hypergraphs." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (2021): 1406–13. http://dx.doi.org/10.17762/turcomat.v12i5.2036.

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Graphs have lots of applications in various domains. They support only pair wise relationships. Hypergraphs does more than graphs. In graph theory, a graph where an edge can join any number of vertices is called as the hyper graph. The corresponding edges are called as hyper edges. The integers used for assignment of labels to the edges and vertices or to only vertices of a graph or to only the edges is called as the graph labeling in this paper we study about factorization and labeling in hyper graphs with the hyper graphs obtained from graphs.

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Alali, Amal S., Shahbaz Ali, Noor Hassan, Ali M. Mahnashi, Yilun Shang, and Abdullah Assiry. "Algebraic Structure Graphs over the Commutative Ring Zm: Exploring Topological Indices and Entropies Using M-Polynomials." Mathematics 11, no. 18 (2023): 3833. http://dx.doi.org/10.3390/math11183833.

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The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from abstract algebra, which deals with algebraic structures such as groups, rings, and fields. If the vertex set of a graph G^ is fully made up of the zero divisors of the modular ring Zn, the graph is said to be a zero-divisor graph. If the products of two vertices are equal to zero under (modn), they are regarded as neighbors. Entropy, a notion taken

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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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Hussain, Muhammad Tanveer, Navid Iqbal, Usman Babar, Tabasam Rashid, and Md Nur Alam. "On Sum Degree-Based Topological Indices of Some Connected Graphs." Mathematical Problems in Engineering 2022 (July 30, 2022): 1–19. http://dx.doi.org/10.1155/2022/2961173.

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In mathematical chemistry, molecular structure of any chemical substance can be expressed by a numeric number or polynomial or sequence of number which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structur

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Mohan, Anandhu, and M. V. Dhanyamol. "Fuzzy Median Graph and its Application in the Deployment of Wireless Sensor Networks." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 33, no. 03 (2025): 279–98. https://doi.org/10.1142/s0218488525500126.

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Median graphs represent a unique category of graphs with significant importance in distance-related concepts within graph theory. This paper aims to expand the concept of median graphs into fuzzy graph theory and investigate whether every fuzzy tree belongs to the classification of the fuzzy median graph. Furthermore, this study characterizes the strong edges in a fuzzy graph using median sets. Additionally, the work delves into the impact of removing bridges and cutvertices on a fuzzy median graph. Finally, the paper proposes a novel model rooted in the concept of the fuzzy median graph for d

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Ahmed, Sohail. "Graph Theory Meets Genetics: Understanding Genome Assembly Through Euler And De Bruijn Graphs." International Journal of Arts, Humanities and Social Studies 6, no. 2 (2024): 14–21. https://doi.org/10.5281/zenodo.10876095.

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This abstract delves into the intricate intersection of Graph Theory and Genetics, focusing on the pivotal role of Eulerian and De Bruijn graphs in deciphering the complexities of genome assembly. Genome assembly, a fundamental challenge in bioinformatics, involves reconstructing the complete DNA sequence of an organism from short, fragmented reads. By leveraging graph theory concepts, specifically Eulerian and De Bruijn graphs, researchers can navigate through this intricate puzzle of genetic information. Eulerian graphs, pioneered by Leonhard Euler in the 18th century, provide a powerful fra

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Slilaty, Daniel. "Coloring permutation-gain graphs." Contributions to Discrete Mathematics 16, no. 1 (2021): 47–52. http://dx.doi.org/10.55016/ojs/cdm.v16i1.62717.

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Correspondence colorings of graphs were introduced in 2018 by Dvořák and Postle as a generalization of list colorings of graphs which generalizes ordinary graph coloring. Kim and Ozeki observed that correspondence colorings generalize various notions of signed-graph colorings which again generalizes ordinary graph colorings. In this note we state how correspondence colorings generalize Zaslavsky's notion of gain-graph colorings and then formulate a new coloring theory of permutation-gain graphs that sits between gain-graph coloring and correspondence colorings. Like Zaslavsky's gain-graph colo

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Broumi, Said, Florentin Smarandache, Mohamed Talea, and Assia Bakali. "An Introduction to Bipolar Single Valued Neutrosophic Graph Theory." Applied Mechanics and Materials 841 (June 2016): 184–91. http://dx.doi.org/10.4028/www.scientific.net/amm.841.184.

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In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.

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Keerthi, G. Mirajkar* Bhagyashri R. Doddamani Priyanka Y. B. "THE REFORMULATED FIRST ZAGREB INDEX OF THE LINE GRAPHS OF THE SUBDIVISION GRAPH FOR CLASS OF GRAPHS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 10 (2016): 144–49. https://doi.org/10.5281/zenodo.159334.

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The reformulated first Zagreb index is the edge version of first Zagreb index of chemical graph theory. The aim of this paper is to obtain an expression for the reformulated first Zagreb index of the some class of graphs such as Tadpole graph, Wheel graph, Ladder graph. Further we also obtain the reformulated first Zagreb index of the line graph, subdivision graph and line graph of subdivision graph for class of graphs.

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