Results 21 to 30 of about 11,183,836 (302)
On the crossing number for Kronecker product of a tripartite graph with path
AKCE International Journal of Graphs and Combinatorics, 2020 The crossing number of a graph G, Cr(G) is the minimum number of edge crossings overall good drawings of G. Among the well-known four standard graph products namely Cartesian product, Kronecker product, strong product and lexicographic product, the one ...
N. Shanthini, J. Baskar Babujee
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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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Software Solution of the Algorithm of the Cyclic-Order Graph [PDF]
Acta Electrotechnica et Informatica, 2018 In this paper we describe by pseudo-code the ``Algorithm of the cyclic-order graph'', which we programmed in MATLAB 2016a and which is also possible to be executed in GNU Octave. We describe program's functionality and its use.
Štefan Berežný +2 more
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Odd Crossing Number and Crossing Number Are Not the Same [PDF]
Discrete & Computational Geometry, 2006 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings, taken over all drawing of \(G\) in the plane. Similarly \(\text{per}(G)\) (respectively \(\text{ocr}(G)\)) denotes the minimum number of pairs of edges which cross at least once (respectively an odd number of times), over all drawings of \(G\) in the plane ...
Pelsmajer, Michael J. +2 more
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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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The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
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The Crossing Number of Join of a Special Disconnected 6-Vertex Graph with Cycle
Mathematics, 2023 The crossing number of a graph G, cr(G), is defined as the smallest possible number of edge-crossings in a drawing of G in the plane. There are almost no results concerning crossing number of join of a disconnected 6-vertex graph with cycle. The main aim
Zongpeng Ding, Xiaomei Qian
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The rectilinear local crossing number of Kn [PDF]
Journal of Combinatorial Theory, 2015 We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3}
B. Ábrego, S. Fernández-Merchant
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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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Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 We define a variant of the crossing number for an embedding of a graphGinto ℝ3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the rectilinear space crossing numbers of pseudo-random graphs.
Bukh, Boris, Hubard, Alfredo
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