The Crossing Numbers Of Cartesian Product Of A Class Graphs

Determining the crossing numbers of graphs has been proved to be NP-complete.There are a few exact results on the crossing numbers of graph class because of its complexity. In many cases,even it is very difficult to find out good bounds of the crossing numbers of graphy .Much effort has been spent on investigating the crossing numbers of complete graphs, complete bipartite graphs and cartesian products graphs. In this paper ,we study the crossing numbers of the cartesian product graph. In chapter two ,we determine the crossing number of the cartesian product of five graphs on 6-vertex with path. In chapter three, we determine the crossing numbers of the cartesian products of S5 and 5 graphs on 6-vertex with path Pn. In chapter four,we determine the crossing number of a 6-vertex graph with the star K1,n, Where S5 and Pn are the star with five edges and the path with n edges ,respectively.