The Study On The Kind Of Perfect Graph

Graph theory is a branch of mathematics,in1736, It has been applied in many different fields in the modern world,such as physics,chemistry,astronomy,geography,biology,as well as in computer science and engineering.As an important direction of graph theory,the research on graceful graph has been a great branch according to its application.Graceful graph is multiplex and flexible,it has remarkable theoretic and applied value.since then,the subject has experienced explosive growth.This thesis is just on studying some problems of graceful graphs.In the first part, some basic definition and usefulness about graph and grace graph are introduced including the main conclusions in this paper.In the next part, A definition has been given of the mi-circle chain graph with a handle and mi-circle chain graph without handle,The gracefulness of the two kind graph when m1,m2,…,mn=0(mod4) is discussed; The graceful labels are given.To mi-circle chain graph without handle,it is a k-graceful graph.the k-graceful labels are given.In addition, the graceful labels when m1,m2,…,mn=0(mod4),mn+1=3(mod4) are given.In the third part,the odd gracefulness and odd strongly harmoniousness for the mi-circle chain figure without handle when n1, m2,…,mn=0(mod4) are proven.In the last part, the odd gracefulness and odd strongly harmoniousness for the cn×p2∪cn×p2when n=2k are proven.