Conjectures About Wheels Without One Edge with Paths and Cycles

Abstract

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products G*+Pn and G*+Cn for the connected graph G* obtained by removing one edge (incident with the dominating vertex) from the wheel W5 on six vertices, and where Pn and Cn are paths and cycles on n vertices, respectively. Finally, we also introduce four new conjectures concerning crossing numbers of the join products of Pn and Cn with Wm∖e obtained by removing one edge (of both possible types) from the wheel Wm on m+1 vertices.

Keywords

• crossing number
• join product
• separating cycle
• wheel
• path
• cycle