两类图的邻点可区别染色问题的研究

摘要

本文引入了图的邻点可区别边染色,图的邻点可区别全染色及k-方图的概念,并定义了一类2维广义格子图H2(G,n,m;k1,k2),且以此类图为主要研究对象.本学位论文共分为四章.
　　第一章是引言部分,包括图论的研究背景和一些与本文相关的预备知识.
　　第二章用构造染色的方法给出了由圈Cl生成的2维广义格子图H2(Cl,n,m;l,l),由完全图K4生成的2维广义格子图H2(K4,n,m;4,4)及由完全二部图Kp,p生成的2维广义格子图H2(Kp,p,n,m;p,p)的邻点可区别边色数,并验证了图的邻点可区别边色数猜想.
　　第三章通过从图的结构出发,用构造染色的方法给出了由圈C5生成的2维广义格子图H2(C5,n,m;5,5)的邻点可区别全色数,并验证了图的邻点可区别全色数猜想.
　　第四章讨论了几类方图的邻点可区别全染色,用构造染色的方法给出了一些方图C3n,C43n,Wkn,Fkn,S2n及S3n,n的邻点可区别全色数,并验证了图的邻点可区别全色数猜想.

目录

封面

声明

目录

英文摘要

中文摘要

Chapter 1 Intro duction and Preliminaries

§1.1 Introduction

§1.2 Preliminaries

Chapter 2 Adjacent vertex-distinguishing prop er edge coloring of one kind of two dimensional generalized grid graphs

§2.1 Adjacent vertex-distinguishing proper edge coloring of one kind of two dimensional generalized grid graph generated by the circle Cl

§2.2 Adjacent vertex-distinguishing proper edge coloring of one kind of two dimensional generalized grid graph generated by the complete graph K4

§2.3 Adjacent vertex-distinguishing proper edge coloring of

Chapter 3 Adjacent vertex-distinguishing total coloring of one kind of two dimensional generalized grid graphs

Chapter 4 Adjacent vertex-distinguishing total coloring of k-th p ower graphs

参考文献

App endix 1 The Published Pap ers During Graduate Study Perio d

App endix 2 Acknowledgements