On the crossing numbers of Cartesian products of stars and graphs on five vertices

Abstract

There are known crossing numbers of Cartesian products of stars with all graphs of order at most four. In this paper we are dealing with the Cartesian products of stars with graphs on five vertices. We give the exact values of crossing numbers for some of these graphs and we summarise all known results concerning crossing numbers of these graphs. In addition, we give the crossing number of the join product of star and the cycle C5 with one additional edge. © Springer-Verlag Berlin Heidelberg 2009.