The crossing numbers of products of path with graphs of order six
Marián Klešč, Jana Petrillová · Discussiones Mathematicae Graph Theory · 2013
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known.For the path P n of length n, the crossing numbers of Cartesian products G P n for all connected graphs G on five vertices are also known.In this paper, the crossing numbers of Cartesian products G P n for graphs G of order six are studied.Let H denote the unique tree of order six with two vertices of degree three.The main contribution is that the crossing number of the Cartesian product H P n is 2(n -1).In addition, the crossing numbers of G P n for fourty graphs G on six vertices are collected.