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Journal articles on the topic 'Graph Theory Approach'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

C.S., Harisha. "Graph Theory Approach to Number Theory Theorems." Journal of Advanced Research in Dynamical and Control Systems 12, no. 01-Special Issue (2020): 568–72. http://dx.doi.org/10.5373/jardcs/v12sp1/20201105.

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2

R, Nandhini, Maheswari V, and Balaji V. "A Graph Theory Approach on Cryptography." Journal of Computational Mathematica 2, no. 1 (2018): 97–104. http://dx.doi.org/10.26524/jcm32.

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3

Ali, Akbar. "Tetracyclic graphs with maximum second Zagreb index: A simple approach." Asian-European Journal of Mathematics 11, no. 05 (2018): 1850064. http://dx.doi.org/10.1142/s179355711850064x.

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In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum

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Yue, Jumei, Yongyi Yan, and He Deng. "Matrix Approach to Formulate and Search k-ESS of Graphs Using the STP Theory." Journal of Mathematics 2021 (July 6, 2021): 1–12. http://dx.doi.org/10.1155/2021/7230661.

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In this paper, the structure of graphs in terms of k-externally stable set (k-ESS) is investigated by a matrix method based on a new matrix product, called semitensor product of matrices. By defining an eigenvector and an eigenvalue of the node subset of a graph, three necessary and sufficient conditions of k-ESS, minimum k-ESS, and k-kernels of graphs are proposed in a matrix form, respectively. Using these conditions, the concepts of k-ESS matrix, minimum k-ESS matrix, and k-kernel matrix are introduced. These matrices provide complete information of the corresponding structures of a graph.

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

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

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Cai, Lei, and Shuiwang Ji. "A Multi-Scale Approach for Graph Link Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 3308–15. http://dx.doi.org/10.1609/aaai.v34i04.5731.

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Deep models can be made scale-invariant when trained with multi-scale information. Images can be easily made multi-scale, given their grid-like structures. Extending this to generic graphs poses major challenges. For example, in link prediction tasks, inputs are represented as graphs consisting of nodes and edges. Currently, the state-of-the-art model for link prediction uses supervised heuristic learning, which learns graph structure features centered on two target nodes. It then learns graph neural networks to predict the existence of links based on graph structure features. Thus, the perfor

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Lee, S. L., and F. Y. Li. "Net sign approach in graph spectral theory." Journal of Molecular Structure: THEOCHEM 207, no. 3-4 (1990): 301–17. http://dx.doi.org/10.1016/0166-1280(90)85032-i.

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

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

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Nair, Aditya G., and Kunihiko Taira. "Network-theoretic approach to sparsified discrete vortex dynamics." Journal of Fluid Mechanics 768 (March 10, 2015): 549–71. http://dx.doi.org/10.1017/jfm.2015.97.

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We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters in

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10

MARTIN, STEPHEN P. "THE GRAPH-REPRESENTATION APPROACH TO TOPOLOGICAL FIELD THEORY IN 2 + 1 DIMENSIONS." International Journal of Modern Physics A 07, no. 03 (1992): 563–89. http://dx.doi.org/10.1142/s0217751x92000259.

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An alternative definition of topological quantum field theory in 2 + 1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but nonlocal observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson-bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wave functions in this "graph representation" approa

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11

Warnaar, D. B., and M. Chew. "Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 1: Graph Generation." Journal of Mechanical Design 117, no. 1 (1995): 112–16. http://dx.doi.org/10.1115/1.2826094.

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Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing, the graph of a structure is transformed into one representing a mechanism. A procedure is present

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12

Asif, Muhammad, Hamad Almohamedh, Muhammad Hussain, Khalid M. Alhamed, Abdulrazaq A. Almutairi, and Sultan Almotairi. "An Approach to the Geometric-Arithmetic Index for Graphs under Transformations’ Fact over Pendent Paths." Complexity 2021 (June 24, 2021): 1–13. http://dx.doi.org/10.1155/2021/3745862.

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Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use. Geometric-arithmetic index is one of the most studied graph invariant to characterize the topological aspects of underlying interconnection networks or graphs. Transformation over graph is also an important tool to define new network of their own choice in computer science. In this work, we discuss transformed family of graphs. Let Γ n k , l b

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Mahmoudzadeh, Houra, and Kourosh Eshghi. "A Metaheuristic Approach to the Graceful Labeling Problem." International Journal of Applied Metaheuristic Computing 1, no. 4 (2010): 42–56. http://dx.doi.org/10.4018/jamc.2010100103.

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In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints. In this paper, the well-known graceful labeling problem of graphs is represented as an optimization problem, and an algorithm based on Ant Colony Optimization metaheuristic is proposed for finding its solutions. In this regard, the proposed algorithm is applied to different classes of graphs and the results are compared with the few exist

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Schneider, Csaba, and Ana C. Silva. "Cliques and colorings in generalized Paley graphs and an approach to synchronization." Journal of Algebra and Its Applications 14, no. 06 (2015): 1550088. http://dx.doi.org/10.1142/s0219498815500887.

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Given a finite field, one can form a directed graph using the field elements as vertices and connecting two vertices if their difference lies in a fixed subgroup of the multiplicative group. If -1 is contained in this fixed subgroup, then we obtain an undirected graph that is referred to as a generalized Paley graph. In this paper, we study generalized Paley graphs whose clique and chromatic numbers coincide and link this theory to the study of the synchronization property in 1-dimensional primitive affine permutation groups.

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15

Wardle, Glenda M. "A GRAPH THEORY APPROACH TO DEMOGRAPHIC LOOP ANALYSIS." Ecology 79, no. 7 (1998): 2539–49. http://dx.doi.org/10.1890/0012-9658(1998)079[2539:agtatd]2.0.co;2.

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16

Reff, Nathan, and Lucas J. Rusnak. "An oriented hypergraphic approach to algebraic graph theory." Linear Algebra and its Applications 437, no. 9 (2012): 2262–70. http://dx.doi.org/10.1016/j.laa.2012.06.011.

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17

SINGER, DENNIS. "BOND GRAPH MODELLING—A GENERAL SYSTEM THEORY APPROACH." International Journal of General Systems 18, no. 1 (1990): 23–35. http://dx.doi.org/10.1080/03081079008935124.

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18

Miller, Benjamin D. "The graph-theoretic approach to descriptive set theory." Bulletin of Symbolic Logic 18, no. 4 (2012): 554–75. http://dx.doi.org/10.2178/bsl.1804030.

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19

HONEYCUTT, CHRISTINA EBEY, and ROY PLOTNICK. "Mathematical analysis of Paleodictyon : a graph theory approach." Lethaia 38, no. 4 (2005): 345–50. http://dx.doi.org/10.1080/00241160500333415.

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20

Şahin, Rıdvan. "An approach to neutrosophic graph theory with applications." Soft Computing 23, no. 2 (2017): 569–81. http://dx.doi.org/10.1007/s00500-017-2875-1.

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21

DIAO, Y., and G. HETYEI. "Relative Tutte Polynomials for Coloured Graphs and Virtual Knot Theory." Combinatorics, Probability and Computing 19, no. 3 (2009): 343–69. http://dx.doi.org/10.1017/s0963548309990484.

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We introduce the concept of a relative Tutte polynomial of coloured graphs. We show that this relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (and hence the Jones polynomial) of a virtual knot can be computed from the relative Tutte polynomial of its face (Tait) graph with some suitable variable substitutions. Our method offers an alternative to the ribbon grap

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22

Ilyutko, D. P., and I. M. Nikonov. "The Diagram Approach in Knot Theory and Applications to Graph Theory." Moscow University Mathematics Bulletin 73, no. 3 (2018): 124–30. http://dx.doi.org/10.3103/s0027132218030087.

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23

Konstantinovsky, Thomas, and Matan Mizrachi. "On Bi-gram Graph Attributes." Computer and Information Science 14, no. 3 (2021): 78. http://dx.doi.org/10.5539/cis.v14n3p78.

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We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a &quot;bi-gram graph&quot; representation of a corpus. The different attributes derived from graph theory are measured and analyzed as unique insights or against other corpus graphs, attributes such as the graph chromatic number and the graph coloring, graph density and graph K-core. We observe a vast domain of tools and algorithms that can be developed on top of the graph representation; creating such a graph proves to be computationally cheap, and much of the heavy lifti

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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 (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, the

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25

Huang, Chien-Hung, Efendi Zaenudin, Jeffrey J. P. Tsai, Nilubon Kurubanjerdjit, Eskezeia Y. Dessie, and Ka-Lok Ng. "Dissecting molecular network structures using a network subgraph approach." PeerJ 8 (August 6, 2020): e9556. http://dx.doi.org/10.7717/peerj.9556.

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Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer n

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26

Breen, Jane, Steve Butler, Nicklas Day, et al. "Computing Kemeny's constant for a barbell graph." Electronic Journal of Linear Algebra 35 (December 9, 2019): 583–98. http://dx.doi.org/10.13001/ela.2019.5175.

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In a graph theory setting, Kemeny’s constant is a graph parameter which measures a weighted average of the mean first passage times in a random walk on the vertices of the graph. In one sense, Kemeny’s constant is a measure of how well the graph is ‘connected’. An explicit computation for this parameter is given for graphs of order n consisting of two large cliques joined by an arbitrary number of parallel paths of equal length, as well as for two cliques joined by two paths of different length. In each case, Kemeny’s constant is shown to be O(n3), which is the largest possible order of Kemeny

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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 (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

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Guze, Sambor. "Graph Theory Approach to the Vulnerability of Transportation Networks." Algorithms 12, no. 12 (2019): 270. http://dx.doi.org/10.3390/a12120270.

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Nowadays, transport is the basis for the functioning of national, continental, and global economies. Thus, many governments recognize it as a critical element in ensuring the daily existence of societies in their countries. Those responsible for the proper operation of the transport sector must have the right tools to model, analyze, and optimize its elements. One of the most critical problems is the need to prevent bottlenecks in transport networks. Thus, the main aim of the article was to define the parameters characterizing the transportation network vulnerability and select algorithms to s

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Geetha, N. K., and P. Sekar. "Graph Theory Matrix Approach – A Qualitative Decision Making Tool." Materials Today: Proceedings 4, no. 8 (2017): 7741–49. http://dx.doi.org/10.1016/j.matpr.2017.07.109.

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30

Srikanth, Rajan. "A Graph Theory-Based Approach for Partitioning Knowledge Bases." ORSA Journal on Computing 7, no. 3 (1995): 286–97. http://dx.doi.org/10.1287/ijoc.7.3.286.

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31

Guze, Sambor. "Graph Theory Approach to Transportation Systems Design and Optimization." TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation 8, no. 4 (2014): 571–78. http://dx.doi.org/10.12716/1001.08.04.12.

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32

Elibol, Armagan, Nuno Gracias, Rafael Garcia, and Jinwhan Kim. "Graph theory approach for match reduction in image mosaicing." Journal of the Optical Society of America A 31, no. 4 (2014): 773. http://dx.doi.org/10.1364/josaa.31.000773.

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33

Elias, Dario, Hebe Campaña, Fernando Poletta, et al. "A graph theory approach to analyze birth defect associations." PLOS ONE 15, no. 5 (2020): e0233529. http://dx.doi.org/10.1371/journal.pone.0233529.

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34

Janakiraman, T. N., and P. V. S. S. R. Chandra Mouli. "Image Segmentation using Euler Graphs." International Journal of Computers Communications & Control 5, no. 3 (2010): 314. http://dx.doi.org/10.15837/ijccc.2010.3.2484.

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This paper presents a new algorithm for image segmentation problem using the concepts of Euler graphs in graph theory. By treating image as an undirected weighted non-planar finite graph (G), image segmentation is handled as graph partitioning problem. The proposed method locates region boundaries or clusters and runs in polynomial time. Subjective comparison and objective evaluation shows the efficacy of the proposed approach in different image domains.

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35

Danilov, I. G., and S. I. Rodzin. "Distributed implementation of the graphs clusterization goodness metrics calculation using mapreduce and vertex-oriented graph processing model." Informatization and communication, no. 3 (May 5, 2020): 31–35. http://dx.doi.org/10.34219/2078-8320-2020-11-3-31-35.

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Goal. Research of the implementation features of the graph clusterization goodness metrics using the vertexoriented graph computing model and MapReduce. Materials and methods. The basic concepts of graph theory were used to define the goodness metrics, and the MapReduce with a vertex-oriented graph-computational approach were used to develop the goodness metrics calculation algorithms. Results. Distributed algorithms for calculating graph clustering goodness metrics are proposed and tested. Conclusion. The results can be used to analyze the quality of the partitioning of large graphs that obta

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Zainullina, R. "Automatic Graph Generation for E-learning Systems." Bulletin of Science and Practice 7, no. 6 (2021): 12–16. http://dx.doi.org/10.33619/2414-2948/67/01.

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The subject of the research is one of the ways of updating modern training systems for solving problems of graph theory, namely, automatic generation of graphs. This approach will reduce the load on the training system database and generate tasks for the user in real-time without updating the bank of tasks. In the course of the work, the advantages and disadvantages of this approach were identified. The most suitable method for the implementation of the research was chosen to represent graphs in electronic computers. The requirements for generated graphs and possible ways of implementing these

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Wang, Shiping, Qingxin Zhu, William Zhu, and Fan Min. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/519173.

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Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering.

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Van Mieghem, Piet. "A Lagrange series approach to the spectrum of the Kite." Electronic Journal of Linear Algebra 30 (February 8, 2015): 934–43. http://dx.doi.org/10.13001/1081-3810.3163.

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A Lagrange series around adjustable expansion points to compute the eigenvalues of graphs, whose characteristic polynomial is analytically known, is presented. The computations for the kite graph P_nK_m, whose largest eigenvalue was studied by Stevanovic and Hansen [D. Stevanovic and P. Hansen. The minimum spectral radius of graphs with a given clique number. Electronic Journal of Linear Algebra, 17:110â117, 2008.], are illustrated. It is found that the first term in the Lagrange series already leads to a better approximation than previously published bounds.

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Devriendt, Karel, and Piet Van Mieghem. "The simplex geometry of graphs." Journal of Complex Networks 7, no. 4 (2019): 469–90. http://dx.doi.org/10.1093/comnet/cny036.

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AbstractGraphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We in

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Alon, Noga. "Choice Numbers of Graphs: a Probabilistic Approach." Combinatorics, Probability and Computing 1, no. 2 (1992): 107–14. http://dx.doi.org/10.1017/s0963548300000122.

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The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). By applying probabilistic methods, it is shown that there are two positive constants c1 and c2 such that for all m ≥ 2 and r ≥ 2 the choice number of the complete r-partite graph with m vertices in each vertex class is between c1r log m and c2r log m. This supplies the solutions of two problems of Erdős, Rubin and Taylor, as it implies that the choice number of almost all the gra

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Shahzadi, Sundas, Musavarah Sarwar, and Muhammad Akram. "Decision-Making Approach with Fuzzy Type-2 Soft Graphs." Journal of Mathematics 2020 (November 17, 2020): 1–25. http://dx.doi.org/10.1155/2020/8872446.

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Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, re

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42

Ouahada, Khmaies, and Hendrik C. Ferreira. "New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis." Communications in Applied and Industrial Mathematics 10, no. 1 (2019): 53–70. http://dx.doi.org/10.1515/caim-2019-0012.

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Abstract A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination o

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Sason, Igal. "A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets in Bipartite Graphs." Entropy 23, no. 3 (2021): 270. http://dx.doi.org/10.3390/e23030270.

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This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn’s information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the

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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 (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

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Jiang, Li, Bu Ying Xie, and Kai Hu. "A Constraint Solving System and Approach Based on Graph Theory and Floating DOF." Applied Mechanics and Materials 444-445 (October 2013): 894–900. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.894.

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Parametric design is a kind of concept to build and analyze models by using parameters or variables rather than digits. Models with different specifications can be achieved by changing the parameter values which are associated with the establishment by labeling the size and adding a variety of constraints. To represent the solving system of plane geometry constraints, the concept of floating DOF is applied based on graph theory to represent the state of the constraints system. And through the establishment of the variable passing rules, changes of the parameters can be shown as rational flow e

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Shi, Hongbo. "A Graph Approach to a Splitting Theorem." Algebra Colloquium 13, no. 01 (2006): 57–66. http://dx.doi.org/10.1142/s1005386706000095.

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By associating a graph to the ring under discussion, we propose a graph approach to extend a well-known ring splitting theorem due to Zaks, and we then describe the global and finitistic dimensions of the ring in the language of the graph.

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Kiremire, Enos Masheija Rwantale. "Graph Theory of Capping Golden Clusters." International Journal of Chemistry 10, no. 1 (2017): 87. http://dx.doi.org/10.5539/ijc.v10n1p87.

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Skeletal numbers and their valences have been extremely useful in analyzing and categorizing clusters especially boranes, carbonyls, and Zintl ions. This approach is being extended to the analysis and categorization of golden clusters. The newly introduced concept of graphing will also be applied to the clusters. The capping symbol Kp = CYC[Mx] which has been restricted to post-closo clusters will be adapted for pre-closo cluster series. The concept of the existence of black holes in the nuclei of capping golden clusters will be introduced and explained.

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48

Sardar, Muhammad Shoaib, Xiang-Feng Pan, Dalal Alrowaili, and Imran Siddique. "Resistance Distance in Tensor and Strong Product of Path or Cycle Graphs Based on the Generalized Inverse Approach." Journal of Mathematics 2021 (August 7, 2021): 1–10. http://dx.doi.org/10.1155/2021/1712685.

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Graph product plays a key role in many applications of graph theory because many large graphs can be constructed from small graphs by using graph products. Here, we discuss two of the most frequent graph-theoretical products. Let G 1 and G 2 be two graphs. The Cartesian product G 1 □ G 2 of any two graphs G 1 and G 2 is a graph whose vertex set is V G 1 □ G 2 = V G 1 × V G 2 and a 1 , a 2 b 1 , b 2 ∈ E G 1 □ G 2 if either a 1 = b 1 and a 2 b 2 ∈ E G 2 or a 1 b 1 ∈ E G 1 and a 2 = b 2 . The tensor product G 1 × G 2 of G 1 and G 2 is a graph whose vertex set is V G 1 × G 2 = V G 1 × V G 2 and a

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49

Rai B, Shamantha, and Shirshu Varma. "An Algorithmic Approach to Wireless Sensor Networks Localization Using Rigid Graphs." Journal of Sensors 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/3986321.

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In this work estimating the position coordinates of Wireless Sensor Network nodes using the concept of rigid graphs is carried out in detail. The range based localization approaches use the distance information measured by the RSSI, which is prone to noise, due to effects of path loss, shadowing, and so forth. In this work, both the distance and the bearing information are used for localization using the trilateration technique. Rigid graph theory is employed to analyze the localizability, that is, whether the nodes of the WSN are uniquely localized. The WSN graph is divided into rigid patches

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

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

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