Group Chromatic Number Of Some Kinds Of Graphs

In this thesis, we study the group chromatic number of some kinds of graphs and the first kind weak total chromatic number of certain graphs. In this paper, we give the group chromatic number of K1,2,n,K1,3,n and AG4. Then we give the first kind weak total chromatic number of total graphs of paths and cycles, and caterpillar graph. Finally, we discuss the group chromatic number of total graphs of paths and total graphs of star and those of Dnk, fans, and the joins of paths and fans.There are four chapters in the thesis:In the first chapter, we introduce the backgrounds and meanings in theory and reality of the first kind weak total coloring and group colorability. Furthermore, we present the definitions, notations and a brief summary of basic content of this thesis. On the other hand, we give the existed results about the first kind weak total coloring and the group coloring.In the second chapter, we study the group chromatic number of some certain graph-s. The definition of alternating group graphs is given in the first part. And in the second part we get the group chromatic numbers of K1,2,n,K1,3,n, and prove Xg(K1,2,n)= 4, n≥3. Xg(K1,3,n)=5, n≥6. In the third part, we get the group chromatic number of AG4, and prove Xg(AG4)= 4.In the third chapter, the first kind weak total chromatic number of total graph of paths and cycles, and caterpillar graph are studied. The definitions of total graph and caterpillar graph are given in the first part. We get the first kind weak total chromatic numbers of total graph of paths and cycles, and caterpillar graph in the second part. The group chromatic numbers of total graphs of paths, total graphs of star, Dnk, fans, and the joins of paths and fans are derived in the third part.In the fourth chapter, we present the conclusions and the future work.