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Academic literature on the topic 'Graph Theory Approach'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Graph Theory Approach"

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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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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4

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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7

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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8

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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