Journal articles: 'Graph theory applications'

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Lloyd, E. Keith, and L. R. Foulds. "Graph Theory Applications." Mathematical Gazette 78, no. 481 (March 1994): 95. http://dx.doi.org/10.2307/3619469.

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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 (June 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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Pirzada, S. "Applications of graph theory." PAMM 7, no. 1 (December 2007): 2070013. http://dx.doi.org/10.1002/pamm.200700981.

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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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Manjula, V. "Graph Applications to Data Structures." Advanced Materials Research 433-440 (January 2012): 3297–301. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.3297.

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This paper presents a topic on Graph theory and its application to data Structures which I consider basic and useful to students in APPLIED MATHEMATICS and ENGINEERING.This paper gives an elementary introduction of Graph theory and its application to data structures. Elements of Graph theory are indispensable in almost all computer Science areas .It can be used in Some areas such as syntactic analysis, fault detection, diagnosis in computers and minimal path problems. The computer representation and manipulation of graph are also discussed so that certain algorithms can be included .A major theme of this paper is to study Graph theory and its Application to data structures Furthermore I hope the students not only learn the course but also develop their analogy perceive, formulate and to solve mathematical programs Thus Graphs especially trees, binary trees are used widely in the representation of data structures this course one can develop mathematical maturity, ability to understand and create mathematical argumentsMethod of derivation is procedure given in the text books with necessary formulae and their application . Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages.

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Anderson, Ian, and H. Walther. "Ten Applications of Graph Theory." Mathematical Gazette 70, no. 453 (October 1986): 245. http://dx.doi.org/10.2307/3615713.

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Abbott, Steve, Jonathan Gross, and Jay Yellen. "Graph Theory and Its Applications." Mathematical Gazette 84, no. 499 (March 2000): 182. http://dx.doi.org/10.2307/3621555.

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Dias, Jerry Ray, and George W. A. Milne. "Chemical Applications of Graph Theory." Journal of Chemical Information and Modeling 32, no. 1 (January 1, 1992): 1. http://dx.doi.org/10.1021/ci00005a600.

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Formanowicz, Piotr, and Krzysztof Tanaś. "A survey of graph coloring - its types, methods and applications." Foundations of Computing and Decision Sciences 37, no. 3 (October 1, 2012): 223–38. http://dx.doi.org/10.2478/v10209-011-0012-y.

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Abstract Graph coloring is one of the best known, popular and extensively researched subject in the field of graph theory, having many applications and conjectures, which are still open and studied by various mathematicians and computer scientists along the world. In this paper we present a survey of graph coloring as an important subfield of graph theory, describing various methods of the coloring, and a list of problems and conjectures associated with them. Lastly, we turn our attention to cubic graphs, a class of graphs, which has been found to be very interesting to study and color. A brief review of graph coloring methods (in Polish) was given by Kubale in [32] and a more detailed one in a book by the same author. We extend this review and explore the field of graph coloring further, describing various results obtained by other authors and show some interesting applications of this field of graph theory.

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Huang, Liangsong, Yu Hu, Yuxia Li, P. K. Kishore Kumar, Dipak Koley, and Arindam Dey. "A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications." Mathematics 7, no. 6 (June 17, 2019): 551. http://dx.doi.org/10.3390/math7060551.

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Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

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Zhang, Xiujun, Muhammed Nadeem, Sarfraz Ahmad, and Muhammad Kamran Siddiqui. "On applications of bipartite graph associated with algebraic structures." Open Mathematics 18, no. 1 (March 2, 2020): 57–66. http://dx.doi.org/10.1515/math-2020-0003.

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Abstract The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures, loops. Graph theory plays an important role in various fields through edge labeling. In this paper, we shall discuss some applications of bipartite graphs, related with Latin squares of Wilson loops, such as metabolic pathways, chemical reaction networks, routing and wavelength assignment problem, missile guidance, astronomy and x-ray crystallography.

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Tatsuoka, Maurice M. "Graph Theory and Its Applications in Educational Research: A Review and Integration." Review of Educational Research 56, no. 3 (September 1986): 291–329. http://dx.doi.org/10.3102/00346543056003291.

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This paper presents a non-technical exposition of graph theory (more particularly, the theory of directed graphs or digraphs), followed by a survey of the literature on applications of graph theory in research in education and related disciplines. The applications include order-theoretic studies of the dimensionality of data sets, the investigation of hierarchical structures in various domains, and cluster analysis. The number of papers applying graph theory was found to be relatively small except in sociology. Possible reasons for the paucity of applications in educational research are discussed, and the value and feasibility of achieving increased use of graph theory in this field are also pointed out.

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Powell, James E., Daniel A. Alcazar, Matthew Hopkins, Tamara M. McMahon, Amber Wu, Linn Collins, and Robert Olendorf. "Graphs in Libraries: A Primer." Information Technology and Libraries 30, no. 4 (December 1, 2011): 157. http://dx.doi.org/10.6017/ital.v30i4.1867.

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Whenever librarians use Semantic Web services and standards for representing data, they also generate graphs, whether they intend to or not. Graphs are a new data model for libraries and librarians, and they present new opportunities for library services. In this paper we introduce graph theory and explore its real and potential applications in the context of digital libraries. Part 1 describes basic concepts in graph theory and how graph theory has been applied by information retrieval systems such as Google. Part 2 discusses practical applications of graph theory in digital library environments. Some of the applications have been prototyped at the Los Alamos National Laboratory Research Library, others have been described in peer-reviewed journals, and still others are speculative in nature. The paper is intended to serve as a high-level tutorial to graphs in libraries.

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Schluchter, Steven. "Applications of ordinary voltage graph theory to graph embeddability." Journal of Graph Theory 87, no. 4 (July 14, 2017): 516–25. http://dx.doi.org/10.1002/jgt.22172.

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Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering." Algorithms 13, no. 9 (August 31, 2020): 214. http://dx.doi.org/10.3390/a13090214.

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To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, there exist families of graphs that have properties that could be exploited for an approximate fast graph spectrum computation. In this work, we aim to identify these families and to provide a divide-and-conquer approach for computing an approximate spectral decomposition of the graph. Using the same decomposition, results on reducing the complexity of graph filtering are derived. These results provide an attempt to leverage the underlying topological properties of graphs in order to devise general computational models for graph signal processing.

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Majeed, Abdul, and Ibtisam Rauf. "Graph Theory: A Comprehensive Survey about Graph Theory Applications in Computer Science and Social Networks." Inventions 5, no. 1 (February 20, 2020): 10. http://dx.doi.org/10.3390/inventions5010010.

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Graph theory (GT) concepts are potentially applicable in the field of computer science (CS) for many purposes. The unique applications of GT in the CS field such as clustering of web documents, cryptography, and analyzing an algorithm’s execution, among others, are promising applications. Furthermore, GT concepts can be employed to electronic circuit simplifications and analysis. Recently, graphs have been extensively used in social networks (SNs) for many purposes related to modelling and analysis of the SN structures, SN operation modelling, SN user analysis, and many other related aspects. Considering the widespread applications of GT in SNs, this article comprehensively summarizes GT use in the SNs. The goal of this survey paper is twofold. First, we briefly discuss the potential applications of GT in the CS field along with practical examples. Second, we explain the GT uses in the SNs with sufficient concepts and examples to demonstrate the significance of graphs in SN modeling and analysis.

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Akram, Muhammad, Maham Arshad, and Shumaiza. "Fuzzy Rough Graph Theory with Applications." International Journal of Computational Intelligence Systems 12, no. 1 (2018): 90. http://dx.doi.org/10.2991/ijcis.2018.25905184.

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Balaban, Alexandru T. "Applications of graph theory in chemistry." Journal of Chemical Information and Modeling 25, no. 3 (August 1, 1985): 334–43. http://dx.doi.org/10.1021/ci00047a033.

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Even-Tzur, Gilad. "Graph Theory Applications to GPS Networks." GPS Solutions 5, no. 1 (July 2001): 31–38. http://dx.doi.org/10.1007/pl00012874.

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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 (December 27, 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. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant.

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KAPOOR, SANJIV, and XIANG-YANG LI. "PROXIMITY STRUCTURES FOR GEOMETRIC GRAPHS." International Journal of Computational Geometry & Applications 20, no. 04 (August 2010): 415–29. http://dx.doi.org/10.1142/s0218195910003360.

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In this paper we study proximity graph structures like Delaunay triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define Voronoi diagrams, Delaunay triangulations, relative neighborhood graphs, Gabriel graphs which are related to the graph structure and then study their complexities when G is a general geometric graph or G is some special graph derived from the application area of wireless networks. Besides being of fundamental interest these structures have applications in topology control for wireless networks.

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Jiang, Huiqin, Ali Asghar Talebi, Zehui Shao, Seyed Hossein Sadati, and Hossein Rashmanlou. "New Concepts of Vertex Covering in Cubic Graphs with Its Applications." Mathematics 10, no. 3 (January 19, 2022): 307. http://dx.doi.org/10.3390/math10030307.

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Graphs serve as one of the main tools for the mathematical modeling of various human problems. Fuzzy graphs have the ability to solve uncertain and ambiguous problems. The cubic graph, which has recently gained a position in the fuzzy graph family, has shown good capabilities when faced with problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Simultaneous application of fuzzy and interval-valued fuzzy membership indicates a high flexibility in modeling uncertainty issues. The vertex cover is a fundamental issue in graph theory that has wide application in the real world. The previous definition limitations in the vertex covering of fuzzy graphs has directed us to offer new classifications in terms of cubic graph. In this study, we introduced the strong vertex covering and independent vertex covering in a cubic graph with strong edges and described some of its properties. One of the motives of this research was to examine the changes in the strong vertex covering number of a cubic graph if one vertex is omitted. This issue can play a decisive role in covering the graph vertices. Since many of the problems ahead are of hybrid type, by reviewing some operations on the cubic graph we were able to determine the strong vertex covering number on the most important cubic product operations. Finally, two applications of strong vertex covering and strong vertex independence are presented.

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VISHVESHWARA, SARASWATHI, K. V. BRINDA, and N. KANNAN. "PROTEIN STRUCTURE: INSIGHTS FROM GRAPH THEORY." Journal of Theoretical and Computational Chemistry 01, no. 01 (July 2002): 187–211. http://dx.doi.org/10.1142/s0219633602000117.

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The sequence and structure of a large body of proteins are becoming increasingly available. It is desirable to explore mathematical tools for efficient extraction of information from such sources. The principles of graph theory, which was earlier applied in fields such as electrical engineering and computer networks are now being adopted to investigate protein structure, folding, stability, function and dynamics. This review deals with a brief account of relevant graphs and graph theoretic concepts. The concepts of protein graph construction are discussed. The manner in which graphs are analyzed and parameters relevant to protein structure are extracted, are explained. The structural and biological information derived from protein structures using these methods is presented.

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Agudelo Muñetón, Natalia, Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, and Isaías David Marín Gaviria. "{0,1}-Brauer Configuration Algebras and Their Applications in Graph Energy Theory." Mathematics 9, no. 23 (November 26, 2021): 3042. http://dx.doi.org/10.3390/math9233042.

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The energy E(G) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q, which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy of a graph. It is worth pointing out that one of the main problems in this theory consists of determining appropriated bounds of these types of energies for significant classes of graphs, digraphs and matrices, provided that, in general, finding out their exact values is a problem of great difficulty. In this paper, the trace norm of a {0,1}-Brauer configuration is introduced. It is estimated and computed by associating suitable families of graphs and posets to Brauer configuration algebras.

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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 (December 24, 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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Joseph, Subin P. "A graph operation and its applications in generating orderenergetic and equienergetic graphs." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 3 (December 2021): 703–15. http://dx.doi.org/10.46793/match.87-3.703j.

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A general graph operation is defined and some of its applications are given in this paper. The adjacency spectrum of any graph generated by this operation is given. A method for generating integral graphs using this operation is discussed. Corresponding to any given graph, we can generate an infinite sequence of pair of equienergetic non-cospectral graphs using this graph operation. Given an orderenergetic graph, it is shown that we can construct two different sequences of orderenergetic graphs. A condition for generating orderenergetic graphs from non-orderenergetic graphs are also derived. This method of constructing connected orderenergetic graphs solves one of the open problem stated in the paper by Akbari et al.(2020).

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Elahi, Kashif, Ali Ahmad, and Roslan Hasni. "Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices." Mathematics 6, no. 12 (December 4, 2018): 301. http://dx.doi.org/10.3390/math6120301.

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Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings Z p 1 p 2 × Z q , where p 1 , p 2 , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings Z p 1 p 2 × Z q .

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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 graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1 and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

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NATH, MILAN, and SOMNATH PAUL. "GRAPH TRANSFORMATION AND DISTANCE SPECTRAL RADIUS." Discrete Mathematics, Algorithms and Applications 05, no. 03 (September 2013): 1350014. http://dx.doi.org/10.1142/s1793830913500146.

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Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees.

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Yang, Hong, Muhammad Siddiqui, Muhammad Ibrahim, Sarfraz Ahmad, and Ali Ahmad. "Computing The Irregularity Strength of Planar Graphs." Mathematics 6, no. 9 (August 30, 2018): 150. http://dx.doi.org/10.3390/math6090150.

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The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs.

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Adali, Tulay, and Antonio Ortega. "Applications of Graph Theory [Scanning the Issue]." Proceedings of the IEEE 106, no. 5 (May 2018): 784–86. http://dx.doi.org/10.1109/jproc.2018.2820300.

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Shea, J. J. "Graph theory and its applications [Book Review]." IEEE Electrical Insulation Magazine 16, no. 2 (March 2000): 36–37. http://dx.doi.org/10.1109/mei.2000.833647.

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Garroway, Colin J., Jeff Bowman, Denis Carr, and Paul J. Wilson. "Applications of graph theory to landscape genetics." Evolutionary Applications 1, no. 4 (September 25, 2008): 620–30. http://dx.doi.org/10.1111/j.1752-4571.2008.00047.x.

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Erdös, P., A. Meir, V. T. Sós, and P. Turán. "On some applications of graph theory, I." Discrete Mathematics 306, no. 10-11 (May 2006): 853–66. http://dx.doi.org/10.1016/j.disc.2006.03.006.

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Liang, Wen-Hai, Wai-Kai Chen, and Shun-Quan Gao. "Applications of lattice theory to graph decomposition." Circuits Systems and Signal Processing 9, no. 2 (June 1990): 181–95. http://dx.doi.org/10.1007/bf01236451.

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Vogelstein, Joshua T., and Carey E. Priebe. "Shuffled Graph Classification: Theory and Connectome Applications." Journal of Classification 32, no. 1 (March 11, 2015): 3–20. http://dx.doi.org/10.1007/s00357-015-9170-6.

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Chen, Dong Li, Yan Zhang, and Chun Hui Ma. "*-Finite Graph and Its Applications." Applied Mechanics and Materials 336-338 (July 2013): 2359–62. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2359.

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By the method of nonstandard analysis, the definition of *-finite graph is given, and necessary and sufficient conditions of *-finite graph are obtained. Further, by the Transfer Principle, we apply the theory of finite graph to *-finite graph, embed given infinite graph into some *-finite graph, and finally obtain the related results of infinite graph.

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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 (April 11, 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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Aydın, Büşra, Nihat Akgüneş, and İsmail Naci Cangül. "On the Wiener Index of the Dot Product Graph over Monogenic Semigroups." European Journal of Pure and Applied Mathematics 13, no. 5 (December 27, 2020): 1231–40. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3745.

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Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving applications. The Wiener index is one of these indices which is equal to the sum of distances between all pairs of vertices in a connected graph. The graph over the nite dot product of monogenic semigroups has recently been dened and in this paper, some results on the Wiener index of the dot product graph over monogenic semigroups are given.

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Borzooei, R. A., R. Almallah, Y. B. Jun, and H. Ghaznavi. "Inverse Fuzzy Graphs with Applications." New Mathematics and Natural Computation 16, no. 02 (July 2020): 397–418. http://dx.doi.org/10.1142/s1793005720500246.

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Rosenfeld [A. Rosenfeld, Fuzzy Graphs, Fuzzy Sets and Their Applications, eds. L. A. Zadeh, K. S. Fu and M. Shimura (Academic Press, New York, 1975), pp. 77–95.] defined the fuzzy relations on the fuzzy sets and developed the structure of fuzzy graph, as a graph with a membership degree (between zero and one) for the vertices and edges such that the membership degree of every edge is less than or equal to the minimum of the membership degree of its endpoints. Although this model of graph has many applications in the real life, it fails to solve a lot of problems, which we can use graph for its representation. This paper aimed to demonstrate a new type of graph with a membership degree (between zero and one) for the vertices and edges so that the membership degree of every edge becomes more than or equals the minimum of the membership degrees of its endpoints. This new type of graph is called inverse fuzzy graph “or” I-fuzzy graph, which can play a role in solving many problems which are not solved by fuzzy graph.

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Wang, Yishu, Ye Yuan, Yuliang Ma, and Guoren Wang. "Time-Dependent Graphs: Definitions, Applications, and Algorithms." Data Science and Engineering 4, no. 4 (September 25, 2019): 352–66. http://dx.doi.org/10.1007/s41019-019-00105-0.

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Abstract A time-dependent graph is, informally speaking, a graph structure dynamically changes with time. In such graphs, the weights associated with edges dynamically change over time, that is, the edges in such graphs are activated by sequences of time-dependent elements. Many real-life scenarios can be better modeled by time-dependent graphs, such as bioinformatics networks, transportation networks, and social networks. In particular, the time-dependent graph is a very broad concept, which is reflected in the related research with many names, including temporal graphs, evolving graphs, time-varying graphs, historical graphs, and so on. Though static graphs have been extensively studied, for their time-dependent generalizations, we are still far from a complete and mature theory of models and algorithms. In this paper, we discuss the definition and topological structure of time-dependent graphs, as well as models for their relationship to dynamic systems. In addition, we review some classic problems on time-dependent graphs, e.g., route planning, social analysis, and subgraph problem (including matching and mining). We also introduce existing time-dependent systems and summarize their advantages and limitations. We try to keep the descriptions consistent as much as possible and we hope the survey can help practitioners to understand existing time-dependent techniques.

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Hayat, Khizar, Muhammad Irfan Ali, Bing-Yuan Cao, and Xiao-Peng Yang. "A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications." Advances in Fuzzy Systems 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/6162753.

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The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets overX(set of all vertices of a graph) andE(set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm.

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Anjum, Rukhshanda, Abdu Gumaei, and Abdul Ghaffar. "Certain Notions of Picture Fuzzy Information with Applications." Journal of Mathematics 2021 (May 4, 2021): 1–8. http://dx.doi.org/10.1155/2021/9931792.

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In this manuscript, the theory of constant picture fuzzy graphs (CPFG) is developed. A CPFG is a generalization of constant intuitionistic fuzzy graph (CIFG) and a special case of picture fuzzy graph (PFG). Additionally, the article includes some basic definitions of CPFG such as totally constant picture fuzzy graphs (TCPFGs), constant function, bridge of CPFG, and their related results. Also, an application of CPFG in Wi-Fi network system is discussed. Finally, a comparison of CPFG is established with that of the CIFG which exhibits the superiority of the proposed idea over the existing ones is discussed.

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Jiang, Huiqin, and Yongsheng Rao. "Connectivity Index in Vague Graphs with Application in Construction." Discrete Dynamics in Nature and Society 2022 (February 15, 2022): 1–15. http://dx.doi.org/10.1155/2022/9082693.

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The vague graph (VG), which has recently gained a place in the family of fuzzy graph (FG), has shown good capabilities in the face of problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Connectivity index (CI) in graphs is a fundamental issue in fuzzy graph theory that has wide applications in the real world. The previous definitions’ limitations in the connectivity of fuzzy graphs directed us to offer new classifications in vague graph. Hence, in this paper, we investigate connectivity index, average connectivity index, and Randic index in vague graphs with several examples. Also, one of the motives of this research is to introduce some special types of vertices such as vague connectivity enhancing vertex, vague connectivity reducing vertex, and vague connectivity neutral vertex with their properties. Finally, an application of connectivity index in the selected town for building hospital is presented.

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Ramachandran, M., and N. Parvathi. "The Medium Domination Number of Lexico Product of Two Paths P2 and Pn." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 426. http://dx.doi.org/10.14419/ijet.v7i4.10.21032.

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Graph theory is a vibrant area in both applications and hypothetical. Graphs can be utilized as a demonstrating device for many problems of realistic consequence. It can be given out as mathematical models to identify a proper graph-theoretic problem. Domination is a hasty sprouting area of research in graph theory, and its various applications are distributed computing and societal networks. Duygu Vargor and Pinar Dundar [1] computed the idea of medium domination number exploited to scrutinize the pair of vertices. This paper study as explored the medium domination number of lexico product of two paths P2 and Pn.

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Nazeer, Saqib, Muhammad Hussain, Fatimah Abdulrahman Alrawajeh, and Sultan Almotairi. "Metric Dimension on Path-Related Graphs." Mathematical Problems in Engineering 2021 (October 29, 2021): 1–12. http://dx.doi.org/10.1155/2021/2085778.

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Graph theory has a large number of applications in the fields of computer networking, robotics, Loran or sonar models, medical networks, electrical networking, facility location problems, navigation problems etc. It also plays an important role in studying the properties of chemical structures. In the field of telecommunication networks such as CCTV cameras, fiber optics, and cable networking, the metric dimension has a vital role. Metric dimension can help us in minimizing cost, labour, and time in the above discussed networks and in making them more efficient. Resolvability also has applications in tricky games, processing of maps or images, pattern recognitions, and robot navigation. We defined some new graphs and named them s − middle graphs, s -total graphs, symmetrical planar pyramid graph, reflection symmetrical planar pyramid graph, middle tower path graph, and reflection middle tower path graph. In the recent study, metric dimension of these path-related graphs is computed.

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Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

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At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that eigenvalues and eigenvectors of several graph matrices can be quickly computed. Spectral graph parameters contain a lot of information on the graph structure (both global and local) including some information on graph parameters that, in general, are computed by exponential algorithms. Moreover, in some applications in data mining, graph spectra are used to encode graphs themselves. The Euclidean distance between the eigenvalue sequences of two graphs on the same number of vertices is called the spectral distance of graphs. Some other spectral distances (also based on various graph matrices) have been considered as well. Two graphs are considered as similar if their spectral distance is small. If two graphs are at zero distance, they are cospectral. In this sense, cospectral graphs are similar. Other spectrally based measures of similarity between networks (not necessarily having the same number of vertices) have been used in Internet topology analysis, and in other areas. The notion of spectral distance enables the design of various meta-heuristic (e.g., tabu search, variable neighbourhood search) algorithms for constructing graphs with a given spectrum (spectral graph reconstruction). Several spectrally based pattern recognition problems appear in many areas (e.g., image segmentation in computer vision, alignment of protein-protein interaction networks in bio-informatics, recognizing hard instances for combinatorial optimization problems such as the travelling salesman problem). We give a survey of such and other graph spectral recognition techniques used in computer sciences.

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Darabian, E., and R. A. Borzooei. "Results on Vague Graphs with Applications in Human Trafficking." New Mathematics and Natural Computation 14, no. 01 (March 2018): 37–52. http://dx.doi.org/10.1142/s1793005718500047.

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A vague graph is a generalized structure of a fuzzy graph that gives more precision, exibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the concepts of eccentricity of nodes, radius and diameter of vague graphs are introduced. The special types of graphs such as eccentrice and antipodal vague graphs are investigated. Then, the relation between eccentrice and antipodal vague graphs are discussed. Finally, an application of eccentrice and antipodal vague graphs in human traffickingn studied.

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Kolman, Pavel, Petr Zach, and Josef Holoubek. "The development of e-learning applications solving problems from graph theory." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 61, no. 7 (2013): 2311–16. http://dx.doi.org/10.11118/actaun201361072311.

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Authors are in long term developing e-learning supports for some parts of Operation Research course. The original purpose was to prepare e-learning supports for students of FBE Mendelu, mainly for part-time form students, who have subscribed Economic mathematical methods course (EMM). Considering decreasing number of lessons on part-time form of study (16 hours in a semester, in comparison to 56 hours in full-time form of study), was for part-time form students even more difficult to fulfill exam requirements. As a help for students there was stage by stage prepared several of programs, they allow self-contained practicing of some linear programming methods. Programs did allow to users step-by-step verify their solution, i.e. whether their calculation are in accordance with algorithm described in lectures. Advantage for the students consists in fact, that each mistake (numerical or algorithmic) they were able to uncover, what contributes to increase of self-study effectiveness and from that resulting higher study motivation. Resulting from existing experience, authors decided to request for a new FRVŠ grant for academic year 2012, focused on e-learning support of selected graph theory problems. Within this project there was developed a tool allowing to make and according to the user needs interactively modify created graphs. On this graph it is possible individually, step by step (in compliance with on lectures presented algorithm) to practice solving of selected graph theory and network analysis problems (e.g. minimal spanning tree, shortest path in a graph, testing for cycles in a graph, critical path method etc.). Project is realized as modular and was realized in Delphi developing tool. Described algorithms are saved in dynamic linked libraries. There for it is very easy to add here new (newly programmed) algorithms. Project results (i.e. project experience obtained from e-learning supports) will be available for all FBE Mendelu members interested in this problematic.

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FOX, JACOB, and JÁNOS PACH. "Applications of a New Separator Theorem for String Graphs." Combinatorics, Probability and Computing 23, no. 1 (October 25, 2013): 66–74. http://dx.doi.org/10.1017/s0963548313000412.

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An intersection graph of curves in the plane is called astring graph. Matoušek almost completely settled a conjecture of the authors by showing that every string graph withmedges admits a vertex separator of size$O(\sqrt{m}\log m)$. In the present note, this bound is combined with a result of the authors, according to which every dense string graph contains a large complete balanced bipartite graph. Three applications are given concerning string graphsGwithnvertices: (i) ifKt⊈Gfor somet, then the chromatic number ofGis at most (logn)O(logt); (ii) ifKt,t⊈G, thenGhas at mostt(logt)O(1)nedges,; and (iii) a lopsided Ramsey-type result, which shows that the Erdős–Hajnal conjecture almost holds for string graphs.

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Journal articles on the topic 'Graph theory applications'

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