Crossing number of Cartesian product of prism and path

Abstract

An m-prism is the Cartesian product of an m-cycle and a path with 2 vertices. We prove that the crossing number of the join of an m-prism () and a graph with k isolated vertices is km for each We then use this result to prove that the crossing number of the Cartesian product of a 5-prism and a path with n vertices is This answers partially the conjecture raised by Peng and Yiew (in 2006) in the affirmative.

Keywords

• crossing number
• cartesian product
• prism
• path