The Crossing Numbers Of The Joins Of Minor Graph With N Isolated Vertices,Path And Cycle

The crossing number plays an important role in the modern graph theory,it originated from the Pal Turan's brick factory problem during the second world war.It has attracted the attention of many experts and carried on the thorough research,and found it is very difficult.To determine the crossing numbers of graphs is proved to be an NP-complete problem by M.R.Garey and D.S.Johnson.So far,the crossing numbers of all five-order with n isolated,path and circle are determined.In this paper,I study the crossing numbers of join graphs on six vertices.From the structural features of the graph,Iobserve and explore the drawing of the graph to obtain a novel result.Filling in a vacancy in the crossing numbers of join graphs on six vertices.And then,the crossing number of this graph with path and circle is determined.In chapter one.We mainly introduce the origin and development of crossing number of graphs,give some basic knowledge and property about the crossing Rumber of graphs.In chapter two.We Mainly study the crossing number of join graph,de-termines that the crossing number of a special six-order graph,respectively.In chapter three.We Determine that the crossing number of the uncon-nected graph H with path and circle.In chapter four.Including the thesis work summary and future research direction.