Results 21 to 30 of about 170,454 (272)
Sufficient Conditions of 6-Cycles Make Planar Graphs DP-4-Colorable
Mathematics, 2022 In simple graphs, DP-coloring is a generalization of list coloring and thus many results of DP-coloring generalize those of list coloring. Xu and Wu proved that every planar graph without 5-cycles adjacent simultaneously to 3-cycles and 4-cycles is 4 ...
Kittikorn Nakprasit +2 more
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Multiscale planar graph generation
Applied Network Science, 2019 The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, due to the scarcity of real-world
Varsha Chauhan +2 more
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Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants
Molecules, 2023 A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices.
Zheng-Qing Chu +5 more
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A Sufficient Condition for Planar Graphs of Maximum Degree 6 to be Totally 7-Colorable
Discrete Dynamics in Nature and Society, 2020 A total k-coloring of a graph is an assignment of k colors to its vertices and edges such that no two adjacent or incident elements receive the same color.
Enqiang Zhu, Yongsheng Rao
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Total Coloring of Claw-Free Planar Graphs
Discussiones Mathematicae Graph Theory, 2022 A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
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Star edge coloring of $ K_{2, t} $-free planar graphs
AIMS Mathematics, 2023 The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
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Recolouring planar graphs of girth at least five [PDF]
arXiv, 2021 For a positive integer $k$, the $k$-recolouring graph of a graph $G$ has as vertex set all proper $k$-colourings of $G$ with two $k$-colourings being adjacent if they differ by the colour of exactly one vertex. A result of Dyer et al. regarding graphs of bounded degeneracy implies that the $7$-recolouring graphs of planar graphs, the $5$-recolouring ...
arxiv
From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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An algorithm of graph planarity testing and cross minimization [PDF]
Computer Science Journal of Moldova, 2007 This paper presents an overview on one compartment from the graph theory, called graph planarity testing. It covers the fundamental concepts and important work in this area.
Vitalie Cotelea, Stela Pripa
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On Computation of Degree-Based Entropy of Planar Octahedron Networks
Journal of Function Spaces, 2022 Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies.
Tian-Le Sun +5 more
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