On The Crossing Numbers Of Join Of Some Special Group

Since 1970s, Paul Turn proposed the concept of the crossing number, and the crossing number of the study has gradually become an important branch of modern graph theory.It is mainly about the research of a picture on a plane or a curved surface, which makes the crossing number the least. Because of its guiding role in practical applications, it has attracted the attention of many experts and scholars at home and abroad. Garey and Johnson have determined that the crossing number of graphs is NP-complete problem, that is, the degree of polynomial complexity of the non deterministic problem.Nowadays, crossing number of graphs is not rich, and it is mainly focused on the graphs with special structure or small order.In this paper, we mainly determine the crossing number of join products of two special five order graphs and the graph of n isolated points.The main structure of this paper is as follows:The first chapter,we introduce the origin and application significance of the crossing number of graphs, and the structure of this paper.In the second chapter, introduce some basic concepts and some lemma and proper ties, which associated with the graph.In the third chapter, the crossing number of join products of a special 5-order graph with n isolated points.In the fourth chapter, the crossing number of join products of C3+ 2K1 with n isolated points.The fifth chapter, summarize our researches and look forward to the work in future.