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Journal articles on the topic 'Application of graph theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Dairina, M. Ihsan, and M. Ramli. "Interactive graph constructing on graph theory application development." Journal of Physics: Conference Series 948 (January 2018): 012064. http://dx.doi.org/10.1088/1742-6596/948/1/012064.

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2

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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Piperski, Alexander. "An application of graph theory to linguistic complexity." Yearbook of the Poznan Linguistic Meeting 1, no. 1 (December 1, 2014): 89–102. http://dx.doi.org/10.1515/yplm-2015-0005.

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Abstract This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.

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Szmytkie, Robert. "Application of graph theory to the morphological analysis of settlements." Quaestiones Geographicae 36, no. 4 (December 1, 2017): 65–80. http://dx.doi.org/10.1515/quageo-2017-0036.

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Abstract In the following paper, the analyses of morphology of settlements were conducted using graph methods. The intention of the author was to create a quantifiable and simple measure, which, in a quantitative way, would express the degree of development of a graph (the spatial pattern of settlement). When analysing examples of graphs assigned to a set of small towns and large villages, it was noticed that the graph development index should depend on: a relative number of edges in relation to the number of nodes (β index), the number of cycles (urban blocks), which evidences the complexity of the spatial pattern of settlement, and the average rank of nodes of a graph, which expresses the degree of complexity of a street network.

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Coufal, Petr, Štěpán Hubálovský, and Marie Hubálovská. "Application of Basic Graph Theory in Autonomous Motion of Robots." Mathematics 9, no. 9 (April 21, 2021): 919. http://dx.doi.org/10.3390/math9090919.

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Discrete mathematics covers the field of graph theory, which solves various problems in graphs using algorithms, such as coloring graphs. Part of graph theory is focused on algorithms that solve the passage through mazes and labyrinths. This paper presents a study conducted as part of a university course focused on graph theory. The course addressed the problem of high student failure in the mazes and labyrinths chapter. Students’ theoretical knowledge and practical skills in solving algorithms in the maze were low. Therefore, the use of educational robots and their involvement in the teaching of subjects in part focused on mazes and labyrinths. This study shows an easy passage through the individual areas of teaching the science, technology, engineering, and mathematics (STEM) concept. In this article, we describe the research survey and focus on the description and examples of teaching in a university course. Part of the work is the introduction of an easy transition from the theoretical solution of algorithms to their practical implementation on a real autonomous robot. The theoretical part of the course introduced the issues of graph theory and basic algorithms for solving the passage through the labyrinth. The contribution of this study is a change in the approach to teaching graph theory and a greater interconnection of individual areas of STEM to achieve better learning outcomes for science students.

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Islam, Sk Rabiul, and Madhumangal Pal. "Hyper-Wiener index for fuzzy graph and its application in share market." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 2073–83. http://dx.doi.org/10.3233/jifs-210736.

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Topological indices have an important role in molecular chemistry, network theory, spectral graph theory and several physical worlds. Most of the topological indices are defined in a crisp graph. As fuzzy graphs are more generalization of crisp graphs, those indices have more application in fuzzy graphs also. In this article, we introduced the fuzzy hyper-Wiener index (FHWI) and studied this index for various fuzzy graphs like path, cycle, star, etc and provided some interesting bounds of FHWI for that fuzzy graph. A lower bound of FHWI is established for n-vertex connected fuzzy graph depending on strength of a strong edges. A relation between FHWI of a tree and its maximum spanning tree is established and this index is calculated for the saturated cycle. Also, at the end of the article, an application in the share market of this index is presented.

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Sebastian, Arya, John N. Mordeson, and Sunil Mathew. "Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking." Mathematics 8, no. 3 (March 16, 2020): 424. http://dx.doi.org/10.3390/math8030424.

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Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

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8

Xue, Hui-Ling, Geng Liu, and Xiao-Hui Yang. "A review of graph theory application research in gears." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 10 (April 16, 2015): 1697–714. http://dx.doi.org/10.1177/0954406215583321.

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Graph theory has been applied to gear train analysis and synthesis for many years, and it is an effective and systematic modeling approach in the design process of gear transmission. Based on more than 100 references listed in this paper, a review about the graph-based method for kinematic and static force analysis, power flow, and mechanical efficiency computation is presented. The method is based on the concept of fundamental circuit corresponding to a basic epicyclic gear train. A 1-dof epicyclic gear train and a two-stage planetary gear train are used to illustrate the application of this method. Besides, isomorphism identification in the synthesis process and enumeration of 1-dof epicyclic gear train graphs are surveyed particularly. Also, the computerized methods for detection of redundant gears and degenerate structures in epicyclic gear trains are reviewed, respectively.

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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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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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11

Tang, Chuan Yin, Xin Yu Hou, Hua Yin, and Ying Zhang. "The Application of Bond Graph Theory on Automobiles Modeling." Applied Mechanics and Materials 120 (October 2011): 339–42. http://dx.doi.org/10.4028/www.scientific.net/amm.120.339.

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Based on the bond graph theory, the acquisition of state equation of vehicle suspension is presented. Set an example to a five degrees of freedom vehicle suspension model ,the simulated results are obtained with the aid of Matlab/Simulink software. Bond graphs are equation based , and are superior to traditional differential equations, they can provide the dynamic digital simulation in time and frequency domain, they can present the static simulation and omit the transition and class-decreasing process which is needed for traditional differential equations.

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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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13

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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14

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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15

Alon, Noga, and P. Erdös. "An Application of Graph Theory to Additive Number Theory." European Journal of Combinatorics 6, no. 3 (September 1985): 201–3. http://dx.doi.org/10.1016/s0195-6698(85)80027-5.

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16

Chakraborty, Anwesha, Trina Dutta, Sushmita Mondal, and Asoke Nath. "Application of Graph Theory in Social Media." International Journal of Computer Sciences and Engineering 6, no. 10 (October 31, 2018): 722–29. http://dx.doi.org/10.26438/ijcse/v6i10.722729.

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Kumar, Suresh, and R. B. S. Yadav. "Application of Graph Theory in Network Analysis." International Journal of Mathematics Trends and Technology 31, no. 2 (March 25, 2016): 44–45. http://dx.doi.org/10.14445/22315373/ijmtt-v31p511.

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18

Breedveld, P. C., R. C. Rosenberg, and T. Zhou. "Bibliography of bond graph theory and application." Journal of the Franklin Institute 328, no. 5-6 (January 1991): 1067–109. http://dx.doi.org/10.1016/0016-0032(91)90069-f.

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19

Eghdami, Hossein, and Majid Darehmiraki. "Application of DNA computing in graph theory." Artificial Intelligence Review 38, no. 3 (May 29, 2011): 223–35. http://dx.doi.org/10.1007/s10462-011-9247-5.

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20

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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21

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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22

Sun, Liang, Yuzhu Zhou, Xuan Chen, and Chuanyu Wu. "Type Synthesis and Application of Gear Linkage Transplanting Mechanisms Based on Graph Theory." Transactions of the ASABE 62, no. 2 (2019): 515–28. http://dx.doi.org/10.13031/trans.13200.

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Abstract. Type synthesis is an important step when designing innovations in mechanisms. To overcome the limitation of traditional gear train transplanting mechanisms in realizing a specific trajectory, a swinging linkage mechanism is introduced into the design of the transplanting mechanism. To design a crop-transplanting gear linkage mechanism (GLM), an automatic synthesis method based on graph theory is proposed in this article. First, the numbers of loops, links, joints and other parameters, along with unlabeled graphs, are calculated based on the structural characteristics of the GLM. The labeled graphs that correspond to the kinematic chain (KC) are then obtained by thickening the edges of the unlabeled graphs, and physically reasonable labeled graphs are derived from identification of the structural rationality of the corresponding structures. Based on the relative motion characteristics of the input and output links of the transplanting mechanisms, criteria for screening the gear linkage mechanisms represented by the labeled graphs are formulated, and the labeled graphs that are suitable for transplanting are calculated to enrich the configurations of the transplanting mechanisms. Finally, two examples are tested to verify the effectiveness of the proposed type synthesis method. Keywords: Gear linkage, Screening, Topological graph, Transplanting mechanism, Type synthesis.

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23

Beaufays, Françoise, and Eric A. Wan. "Relating Real-Time Backpropagation and Backpropagation-Through-Time: An Application of Flow Graph Interreciprocity." Neural Computation 6, no. 2 (March 1994): 296–306. http://dx.doi.org/10.1162/neco.1994.6.2.296.

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We show that signal flow graph theory provides a simple way to relate two popular algorithms used for adapting dynamic neural networks, real-time backpropagation and backpropagation-through-time. Starting with the flow graph for real-time backpropagation, we use a simple transposition to produce a second graph. The new graph is shown to be interreciprocal with the original and to correspond to the backpropagation-through-time algorithm. Interreciprocity provides a theoretical argument to verify that both flow graphs implement the same overall weight update.

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Kalathian, Shriram, Sujatha Ramalingam, Sundareswaran Raman, and Narasimman Srinivasan. "Some topological indices in fuzzy graphs." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 6033–46. http://dx.doi.org/10.3233/jifs-189077.

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A fuzzy graph is one of the versatile application tools in the field of mathematics, which allows the user to easily describe the fuzzy relation between any objects. The nature of fuzziness is favorable for any environment, which supports to predict the problem and solving it. Fuzzy graphs are beneficial to give more precision and flexibility to the system as compared to the classical model (i.e.,) crisp theory. A topological index is a numerical quantity for the structural graph of the molecule and it can be represented through Graph theory. Moreover, its application not only in the field of chemistry can also be applied in areas including computer science, networking, etc. A lot of topological indices are available in chemical-graph theory and H. Wiener proposed the first index to estimate the boiling point of alkanes called ‘Wiener index’. Many topological indices exist only in the crisp but it’s new to the fuzzy graph environment. The main aim of this paper is to define the topological indices in fuzzy graphs. Here, indices defined in fuzzy graphs are Modified Wiener index, Hyper Wiener index, Schultz index, Gutman index, Zagreb indices, Harmonic index, and Randić index with illustrations. Bounds for some of the indices are proved. The algorithms for distance matrix and MWI are shown. Finally, the application of these indices is discussed.

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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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26

Reibenspies, J. H. "Enumeration and Classification of Anomaly/Peak Bases in Two-Dimensional Intensity Histograms. Application of Graph Theory to Crystallographic Data Imaging." Journal of Applied Crystallography 29, no. 3 (June 1, 1996): 241–45. http://dx.doi.org/10.1107/s0021889895015354.

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Bragg-event peaks, spikes, intensity streaks and other anomalies generate abnormal regions in two-dimensional intensity histograms from area-detector images. Examination of the shapes of these regions can contribute to the identification of the types of phenomena that generated them. The points that define the anomaly bases, when connected with imaginary lines, form unique graphs. Individual graphs, in turn, can be enumerated by employing graph-theoretical notation and the graph shapes classified. The number of lines in any given graph can also be determined by summing the degrees of the graph points and dividing by two. The ratio of the number of lines per point is a direct indication of the shape of the anomaly base. Long linear and curved shapes, like those associated with intensity streaks and powder rings, will have small lines-per-point ratios, while compact round, square or oval shapes, similar to those belonging to Bragg-event peaks, will have larger lines-per-point ratios. For any given number of points (Np ), for any given graph, the minimum number of lines (q) will equal Np − 1, while the maximum number of lines (q max, Np ) is determined from a round-shaped graph. A graph-shape parameter (GS) can thus be defined as (q − Np − 1)/(q max. Np − Np − 1), where a value near one indicates a round graph shape and a value near zero indicates a linear graph shape. The application of graph-theoretical techniques to anomaly bases can thus provide insight into the nature of the intensities distributed throughout the two-dimensional crystallographic data image.

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E. Lee, Barton. "Consensus and voting on large graphs: An application of graph limit theory." Discrete & Continuous Dynamical Systems - A 38, no. 4 (2018): 1719–44. http://dx.doi.org/10.3934/dcds.2018071.

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Malik, Hafsa, Muhammad Akram, and Florentin Smarandache. "Soft Rough Neutrosophic Influence Graphs with Application." Mathematics 6, no. 7 (July 18, 2018): 125. http://dx.doi.org/10.3390/math6070125.

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In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate these concepts with examples, and investigate some of their properties. We solve the decision-making problem by using our proposed algorithm.

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Sawollek, Jörg. "Embeddings of 4-Regular Graphs into 3-Space." Journal of Knot Theory and Its Ramifications 06, no. 05 (October 1997): 727–49. http://dx.doi.org/10.1142/s0218216597000406.

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Embeddings of 4-regular graphs into 3-space are examined by studying graph diagrams, i.e. projections of embedded graphs to an appropriate plane. New diagrams can be constructed from the old ones by replacing graph vertices with rational tangles, and these diagrams lead to topological invariants of embedded graphs. The new invariants are calculated for some examples, in particular for classes of alternating diagrams of the figure-eight graph. As an application, it is shown that these diagrams have minimal crossing number, which gives generalizations to some of the so-called Tait conjectures.

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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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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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Sreejil, K., and R. Balakumar. "ANALYSIS OF FUZZY GRAPH THEORY AND ITS APPLICATION." Advances in Mathematics: Scientific Journal 9, no. 3 (June 21, 2020): 1231–38. http://dx.doi.org/10.37418/amsj.9.3.49.

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P, LALITHA. "Application of graph theory in diagnosis of malocclusion." Journal of Management and Science 7, no. 1 (June 30, 2017): 126–34. http://dx.doi.org/10.26524/jms.2017.15.

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The objective of this article is to use graph theory as a modality to simplify and explain the properties of complex biological processes in orthodontics so as to aid in diagnosis and treatment planning. Network analysis, an innovative statistical tool, provides a new approach to understand complex problems. It is a graphical model that encodes probabilistic relationship among variables of interest. When used incombination with statistical technique this graphic model which illustrates the causal relationship among different variables and hence can be used to gain understanding about a problem and predict the consequences of intervention. Orthodontics deals with correction of malocclusion and other dentofacial anomalies which usually have a complex multifactorial etiology. Diagnosis and treatment planning may need the correlation of the clinical, radiographic, and the functional data. The use of graph theory to analyse these datas can drastically reduce the complexity of the pertaining problem. The topology of the dentofacial system obtained by network analysis could allow orthodontists to visually evaluate and anticipate the co-occurrence of auxological anomalies during individual craniofacial growth and possibly localize reactive sites for a therapeutic approach to malocclusion. This article discusses the scope of graph theory and its use in dentistry in general and orthodontics in particular.

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Ru, A. "AN APPLICATION OF GRAPH THEORY IN FABRIC DESIGN." Research Journal of Textile and Apparel 5, no. 2 (May 2001): 41–45. http://dx.doi.org/10.1108/rjta-05-02-2001-b004.

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Qi, Xiao‐Guang, and B. Kent Lall. "Application of Graph Theory to Computer‐Assisted Mapping." Journal of Surveying Engineering 115, no. 4 (November 1989): 380–89. http://dx.doi.org/10.1061/(asce)0733-9453(1989)115:4(380).

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36

Bunn, A. G., D. L. Urban, and T. H. Keitt. "Landscape connectivity: A conservation application of graph theory." Journal of Environmental Management 59, no. 4 (August 2000): 265–78. http://dx.doi.org/10.1006/jema.2000.0373.

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37

Chen, Jinkun, and Jinjin Li. "An application of rough sets to graph theory." Information Sciences 201 (October 2012): 114–27. http://dx.doi.org/10.1016/j.ins.2012.03.009.

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38

Jog, S. R., and Raju Kotambari. "On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs." Journal of Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5906801.

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Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

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Ma, Ming Yue, and Xiang Yang Xu. "A Novel Algorithm for Enumeration of the Planetary Gear Train Based on Graph Theory." Advanced Materials Research 199-200 (February 2011): 392–99. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.392.

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As well known, graph theory is a powerful tool for mechanism design. The enumeration of planet gear trains can be converted the synthesis of graphs while a planetary gear train is converted to a graph. During the enumeration of graphs, the problem of isomorphism should be solved. This paper proposes a novel algorithm used to generate non-isomorphism graphs and thereby omits the part of isomorphism detection. The vertex characteristic is firstly defined in this paper that is the core of the enumeration algorithm. This paper also gives an example of the application for the algorithm.

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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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Ratheesh, K. P. "On Soft Graphs and Chained Soft Graphs." International Journal of Fuzzy System Applications 7, no. 2 (April 2018): 85–102. http://dx.doi.org/10.4018/ijfsa.2018040105.

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Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by parametrization process. In this article, the authors explore the concepts of soft relation on a soft set, soft equivalence relation on a soft set, soft graphs using soft relation, vertex chained soft graphs and edge chained soft graphs and investigate various types of operations on soft graphs such as union, join and complement. Also, it is established that every fuzzy graph is an edge chained soft graph.

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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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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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Zhang, Zhiqiang, Zeshan Saleem Mufti, Muhammad Faisal Nadeem, Zaheer Ahmad, Muhammad Kamran Siddiqui, and Muhammad Reza Farahani. "Computing Topological Indices for Para-Line Graphs of Anthracene." Open Chemistry 17, no. 1 (November 13, 2019): 955–62. http://dx.doi.org/10.1515/chem-2019-0093.

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AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

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Boaventura-Netto, Paulo Oswaldo. "Ranking graph edges by the weight of their spanning arborescences or trees." Pesquisa Operacional 28, no. 1 (April 2008): 59–73. http://dx.doi.org/10.1590/s0101-74382008000100004.

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A result based on a classic theorem of graph theory is generalized for edge-valued graphs, allowing determination of the total value of the spanning arborescences with a given root and containing a given arc in a directed valued graph. A corresponding result for undirected valued graphs is also presented. In both cases, the technique allows for a ranking of the graph edges by importance under this criterion. This ranking is proposed as a tool to determine the relative importance of the edges of a graph in network vulnerability studies. Some examples of application are presented.

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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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Ramprasad, Ch, P. L. N. Varma, S. Satyanarayana, and N. Srinivasarao. "Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph." Advances in Fuzzy Systems 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/3817469.

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Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.

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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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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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