Calculating Crossing Numbers of Graphs Using Their Redrawings

Abstract

The main aim of the paper is to give the crossing number of the join product G*+Dn. The connected graph G* of order six is isomorphic to K3,3\e obtained by removing one edge from the complete bipartite graph K3,3, and the discrete graph Dn consists of n isolated vertices. The proofs were carried out with the help of several possible redrawings of the graph G* with respect to its many symmetries.

Keywords

• graph
• optimal drawing
• crossing number
• join product
• rotation
• redrawing