The crossing numbers of Cartesian products of paths with 5-vertex graphs

被引：30

作者：

Klesc, M ^{[1
]}

机构：

[1] Tech Univ, Fac Elect Engn & Informat, Dept Math, Kosice 04200, Slovakia

来源：

DISCRETE MATHEMATICS | 2001年 / 233卷 / 1-3期

关键词：

graph; drawing; crossing number; path; Cartesian product;

D O I：

10.1016/S0012-365X(00)00251-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For two graphs defined from K-5 by removing one edge or two nonadjacent edges we prove that the crossing number of Cartesian product of the graph with the path of length n is 4n and 3n-1, respectively These results complete the crossing numbers list of Cartesian products of ail 5-vertex graphs with paths. We also give a description of Cartesian products of 5-vertex graphs with cycles and stars, whose crossing numbers are known. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：353 / 359

页数：7

共 50 条

[21] THE BINDING NUMBERS OF SOME CARTESIAN PRODUCTS OF GRAPHS
MICHALAK, D
DISCRETE MATHEMATICS, 1994, 131 (1-3) : 363 - 366
[22] Vertex-neighbor-toughness of the Cartesian Products of paths and cycles
Wei, Zongtian
Yang, Jingting
Li, Yinkui
Yue, Chao
ARS COMBINATORIA, 2019, 147 : 63 - 78
[23] On vertex irregular total labelings of cartesian products of two paths
Bokhary, Syed Ahtsham ul Haq
Ahmad, Ali
Imran, M.
UTILITAS MATHEMATICA, 2013, 90 : 239 - 249
[24] The crossing number of Cartesian products of complete bipartite graphs K2,m with paths Pn
Ling, Tang
Shengxiang, Lv
Yuanqiu, Huang
GRAPHS AND COMBINATORICS, 2007, 23 (06) : 659 - 666
[25] The Crossing Number of Cartesian Products of Complete Bipartite Graphs K2,m with Paths Pn
Tang Ling
Lv Shengxiang
Huang Yuanqiu
Graphs and Combinatorics, 2007, 23 : 659 - 666
[26] Optimal orientations of vertex-multiplications of Cartesian products of graphs
Wong, H. W. Willie
Tay, E. G.
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2022, 83 : 109 - 128
[27] Distinguishing numbers of Cartesian products of multiple complete graphs
Fisher, Michael J.
Isaak, Garth
ARS MATHEMATICA CONTEMPORANEA, 2012, 5 (01) : 159 - 173
[28] On Domatic and Total Domatic Numbers of Cartesian Products of Graphs
P. Francis
Deepak Rajendraprasad
Bulletin of the Malaysian Mathematical Sciences Society, 2023, 46
[29] On Domatic and Total Domatic Numbers of Cartesian Products of Graphs
Francis, P.
Rajendraprasad, Deepak
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2023, 46 (03)
[30] Efficient Solvability of the Weighted Vertex Coloring Problem for Some Hereditary Class of Graphs with 5-Vertex Prohibitions
Gribanov D.V.
Malyshev D.S.
Mokeev D.B.
Journal of Applied and Industrial Mathematics, 2020, 14 (03) : 480 - 489

← 1 2 3 4 5 →