The Problem Of Vertex Distinguishing Coloring Of Graphs

The coloring theory of graph is one of the important theory in graphs.Recently, many kinds of coloring problems are presented,such as the vertex distinguishing edge coloring and adjacent vertex distinguishing coloring are all the extension of coloring theory.In this paper we deal with some graphs in vertex distinguishing edge coloring or adjacent vertex distinguishing coloring problems by using the induction method.This thesis consists of three chapters.In the first chapter,we introduce some problems,backgrounds and the definition of vertex distinguishing coloring.In the second chapter,we mainly deal with the vertex distinguishing edge coloring problem.In 1993,A.C.Burrishe and R.H.Schelp presented the new definition and conjecture of vertex distinguishing coloring,and obtained some results.In this chapter, we investigate the vertex distinguishing edge coloring in 3-regular Halin graph and Halin graph withΔ(G)≥4.Also,we obtain the vertex distinguishing equitable edge chromatic number of S_n∨S_n,F_n∨F_n,W_n∨W_n.In the third chapter,we study the adjacent vertex distinguishing total coloring problem.Based on the theory of vertex distinguishing coloring,professor Zhang Zhongfu presented the new definition and conjecture of adjacent vertex distinguishing coloring. In this chapter,we investigate the adjacent vertex distinguishing total chromatic number on 2-connected outer plane graph withΔ(G) = 7.