The Crossing Number Of The Join Graph Of A Disconnected Graph On Six Vertices With NK₁

The crossing number of a graph is a significant notion,originated from Modern Graph Theory,which starts at the 1940s,since Paul Turn proposed the concept of the crossing number,the crossing number of the study has gradually become an important orientation of moderm graph theory,and it is difficulty in the forefront of Topological Graph Theory.The crossing number of a graph mainly studies the minimum crossing number of the graph's best drawing on he plane or curved surface,it's a characterization of a graph of non-plane of an important parameter.Due to the use of the design of electronic circuits,the identification and repaint of sketch and the graphical representation of DNA in biology engineer and so on,so many professors and scholars home and aborad have engaged in the investigation in this field.But Garey and Johnson have proved that in general the problem to obtain the crossing number of a graphs is NP-complete problem,that is,the degree of polynomial complexity of the non deteministic problem.Therefore,few achievements of the studies about the crossing number of graphs we' ve had for now,and it is mainly focused on the graphs with special structure or small order,but there are few achievements of the studies about the crossing number of disconnected graph.In this paper,we have got the crossing number of the join graph of a disconnected graph on six vertices with the graph of n isolated points.One.We introduce the origins and backgrounds of the crossing number,and the structure of this paper.Two.Introduce some basic concepts and some lemma and properties,which associated with the graph.Three.On the crossing number of the join graph of a disconnected graph on six vertices with n isolated points,and sum up the main conditions of the testify.Four.Summarize our researches and look forward to the work in future.