On the Crossing Number of the Cartesian Product of a \(6\)-Vertex Graph with\(S\)

Jing Wang1, Lixi Zhang2, Yuanqiu Huang2
1Department of Mathematics and Information Sciences, Changsha University, Changsha 410003, P.R.China,
2College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China

Abstract

Computing the crossing number of a given graph is, in general, an elusive problem, and only the crossing numbers of a few families of graphs are known. Most of them are the Cartesian products of special graphs. This paper determines the crossing number of the Cartesian product of a 6-vertex graph with the star \(S_n\).