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Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs
Mathematics, 2023 Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory.
Jana Fortes, Michal Staš
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The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five
Mathematics, 2021 The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph K1,1,3\e obtained by removing one edge e incident with some ...
Michal Staš
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Exploring the Crossing Numbers of Three Join Products of 6-Vertex Graphs with Discrete Graphs
MathematicsThe significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data ...
Michal Staš, Mária Švecová
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Molecules, 2018 The Cartesian product and join are two classical operations in graphs. Let dL(G)(e) be the degree of a vertex e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and geometric arithmetic (GAe) indices of G are defined as
Xiujun Zhang +3 more
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The crossing numbers of join products of paths with three graphs of order five [PDF]
Opuscula Mathematica, 2022 The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices.
Michal Staš, Mária Švecová
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Every graph is local antimagic total and its applications [PDF]
Opuscula Mathematica, 2023 Let \(G = (V,E)\) be a simple graph of order \(p\) and size \(q\). A graph \(G\) is called local antimagic (total) if \(G\) admits a local antimagic (total) labeling. A bijection \(g : E \to \{1,2,\ldots,q\}\) is called a local antimagic labeling of \(G\)
Gee-Choon Lau +2 more
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Distance antimagic labelings of product graphs
Electronic Journal of Graph Theory and Applications, 2023 A graph G is distance antimagic if there is a bijection f : V(G)→{1, 2, …, |V(G)|} such that for every pair of distinct vertices x and y applies w(x)≠w(y), where w(x)=Σ z ∈ N(x)f(z) and N(x) is the neighbourhood of x, i.e., the set of all vertices ...
Risma Yulina Wulandari +1 more
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The crossing numbers of join products of eight graphs of order six with paths and cycles
Karpatsʹkì Matematičnì Publìkacìï, 2023 The crossing number $\mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths ...
M. Staš
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On the crossing numbers of join products of five graphs of order six with the discrete graph [PDF]
Opuscula Mathematica, 2020 The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product \(G^{\ast} + D_n\), where the disconnected graph \(G^{\ast}\) of order six consists of ...
Michal Staš
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ALTERNATIVE PROOF ON THE CROSSING NUMBER OF K1,1,3,N [PDF]
Acta Electrotechnica et Informatica, 2019 The main aim of the paper is to give the crossing number of join product G+Dn for the connected graph G of order five isomorphic with the complete tripartite graph K1,1,3, where Dn consists on n isolated vertices.
Michal STAS
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