关于图的邻点可区别全色数的上界研究  

On an upper bound for adjacent vertex distinguishing total chromatic number of graphs

作　　者：刘利群[1] 陈祥恩[2] 

机构地区：[1]长江大学信息与数学学院,湖北荆州434023 [2]西北师范大学数学与信息科学学院,甘肃兰州730079

出　　处：《纯粹数学与应用数学》2012年第6期744-748,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(61163037;61163054)

摘　　要：图G的邻点可区别全染色是指G存在一个正常全染色f使得任意相邻两点有不同的色集合.本文主要研究邻点可区别正常全色数的上界,目前邻点可区别全染色的一个较好的上界是△+C+20√△ln△,本文用概率方法改进了这个结果,得到了邻点可区别全色数的一个较小上界△+C+3.A proper total coloring of the graph G is called adjacent vertex distinguishing total coloring, for any two adjacent vertices u, v ∈ V（G）, we have C（u）≠ C（v）, where C（u） is called color set of vertex u. In this paper, we study the upper bound on the adjacent vertex distinguishing total chromatic number. A ＋ C ＋ 20√ΔlnΔ is a good conclusion of the upper bound on the adjacent vertex distinguishing total chromatic number of graphs up till now. By probability method, we obtained the conclusion that a upper bound on the adjacent vertex distinguishing total chromatic number is A ＋ C ＋ 3 in some condition in this paper.

关 键 词：邻点可区别全染色 邻点可区别全色数 上界 

分 类 号：O157.5[理学—数学]