The Crossing Number Of A Class Of Special Fifth-order Graphs And The Joint Graphs Of N Isolated Vertices

The crossing number of graphs is an important parameter.The crossing number of graph is mainly about the research of a picture on a plane,which makes the crossing number the least.But so far,there is no effective algorithm that can determine the number of intersections of arbitrary graphs.In 1983 Garey and Johnson had proved that the problem of determining the crossing number of graphs is a NP-complete problem.Due to its difficulty,the research of experts and scholars at home and abroad is mainly focus on the graph with small-order or special structures.Based on a forbidden sub-drawing method ofK_5,5,the thesis uses the method of logical reasoning to prove the crossing number of a class of special fifth-order graphs and the joint graphs of n isolated vertices.The thesis is structure as follows:In chapter 1,we introduce the application background,research status at home and abroad.In chapter 2,we introduce some basic definitions and main properties of the cross number of the graph.In chapter 3,we introduce some important lemmas required for the proof of this thesis,and then proves the main conclusions.In chapter 4,according to the conclusion of Chapter 3 and the specific graphs,we have obtained the number of the crossing number of a class of special fifth-order graphs and the joint graphs of n isolated vertices.In chapter 5,we summarize the main content of this article and its advantages in research methods,as well as further research issues.