On The Crossing Numbers Of Graphs And Crossing Critical

The crossing number of a graph is a significant notion, originated from Modern Graph Theory, which is studying how to draw a graph on a plan with the least crossings. For the practicality in theory field, attracting many scholars’ attentions and studies. But to obtain the crossing number of general graphs is NP-Complete problem. Therefore, few achievements of the studies about the crossing number of graphs we’ve had for now. But there are quite some conclusions of the crossing number of some special graphs and single graphs we have obtained. At the same time, many scholars at home and abroad have got many related properties attached to the crossing number of a graph, such as critical-crossing graph,in the process of studying the crossing number.In this paper, we have proved that the crossing number of S5V Cn and constructs a4-regular crossing-critical graph by replacing vertex of a graph with another graph. What’s more, we obtain the crossing number of a graph which is obtained by replacing each edge with K4,4K4,4-e.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. Proved that the crossing number of S5∨Cn.Four. Constructs a4-regular crossing-critical graph by replacing vertex of a graph with another graph.Five. We make some conclusions of our research work and put forward some relative problems which we will go ahead.