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The Crossing Number of Join of the Generalized Petersen Graph P(3, 1) with Path and Cycle
Discussiones Mathematicae Graph Theory, 2018 There are only few results concerning the crossing numbers of join of some graphs. In this paper, the crossing numbers of join products for the generalized Petersen graph P(3, 1) with n isolated vertices as well as with the path Pn on n vertices and with
Ouyang Zhang Dong +2 more
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Boundary slopes of 2-bridge links determine the crossing number [PDF]
, 2006 A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M.
Hoste, Jim E., Shanahan, Patrick D.
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Counting Hamiltonian Cycles in 2-Tiled Graphs
Mathematics, 2021 In 1930, Kuratowski showed that K3,3 and K5 are the only two minor-minimal nonplanar graphs. Robertson and Seymour extended finiteness of the set of forbidden minors for any surface.
Alen Vegi Kalamar +2 more
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The crossing number of the generalized Petersen graph P(3k,k) in the projective plane
AKCE International Journal of Graphs and Combinatorics, 2023 The crossing number of a graph G in a surface Σ, denoted by [Formula: see text], is the minimum number of pairwise intersections of edges in a drawing of G in Σ. Let k be an integer satisfying [Formula: see text], the generalized Petersen graph [Formula:
Jing Wang, Zuozheng Zhang
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Minor-monotone crossing number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The minor crossing number of a graph $G$, $rmmcr(G)$, is defined as the minimum crossing number of all graphs that contain $G$ as a minor. We present some basic properties of this new minor-monotone graph invariant.
Drago Bokal +2 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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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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Cyclic Permutations in Determining Crossing Numbers
Discussiones Mathematicae Graph Theory, 2022 The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied.
Klešč Marián, Staš Michal
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Skewness and the crossing numbers of graphs
AIMS Mathematics, 2023 The skewness of a graph $ G $, $ sk(G) $, is the smallest number of edges that need to be removed from $ G $ to make it planar. The crossing number of a graph $ G $, $ cr(G) $, is the minimum number of crossings over all possible drawings of $ G $. There
Zongpeng Ding
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On the crossing number of join product of the discrete graph with special graphs of order five
Electronic Journal of Graph Theory and Applications, 2020 The main aim of the paper is to give the crossing number of join product G+Dn for the disconnected graph G of order five consisting of the complete graph K4 and of one isolated vertex.
Michal Staš
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