On The Crossing Numbers Of Cartesian Products Of 5-vertices Graphs With Stars

Knowing that determining the crossing numbers of graphs is NP-complete (see [1]). There are a few exact results on the crossing numbers of graphs for its complexity. Even in many cases, it is very difficult to find upper or lower bounds of the crossing numbers of graphs.In this paper, we study the crossing numbers of the Cartesian products of complete graph K₅ and its subgraph K₅\e with stars S_n.Chapter one, introducing the backgrounds of the crossing numbers of graphs, its development around the world, the meanings of the research, and the problems we will solve.Chapter two, giving some conceptions and properties, and introducing the required knowledges about crossing numbers when read this paper.Chapter three, determining the crossing numbers of the Cartesian products of K₅\e with stars S_n.Chapter four, determining the crossing numbers of the Cartesian products of complete graph K₅ with stars S_n.Chapter five, describing some questions when researching into this problem, and the direction I will go ahead.