ON THE CROSSING NUMBER OF THE JOIN OF THE WHEEL ON FIVE VERTICES WITH THE DISCRETE GRAPH

Abstract

We give the crossing number of the join product$W_{4}+D_{n}$, where$W_{4}$is the wheel on five vertices and$D_{n}$consists of$n$isolated vertices. The proof is based on calculating the minimum number of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph$W_{4}$and from the set of subgraphs which cross the edges of$W_{4}$exactly once.