图K_(2n+1)\E(W_m)的点可区别全染色  

Vertex Distinguishing Total Coloring of K_(2n+1)\E(W_m)

作　　者：李沐春[1] 文飞[1] 张威[2] 孙亮萍[1] 

机构地区：[1]兰州交通大学应用数学研究所,甘肃兰州730070 [2]华南师范大学物理与电信工程学院,广东广州510631

出　　处：《南开大学学报（自然科学版）》2011年第5期47-53,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11061017);甘肃省自然科学基金(1010RJZA075)

摘　　要：图的点可区别全染色是一个正常全染色,并且满足任意两个不同点所染的颜色与相关联元素所染的颜色构成的色集合不同,其所用的最少颜色数被称为图的点可区别全色数.给出了奇阶完全图K2n+1去掉子图Wm的边集E(Wm)之后较为系统地染色方法,并研究了图K2n+1\E(Wm)的点可区别全染色,得到了其点可区别全色数和相关猜想,其中n≥2,m≥3.A proper total coloring of a simple graph G is called vertex distinguishing total coloring if for any two distinct vertices u and v in G,the set of colors assigned to u and the elements incident to u differs from the set of colors incident to v.The minimal number of colors required for a vertex distinguishing total coloring of G is called the vertex distinguishing total chromatic number.A more systematic coloring method through complete graph K2n＋1 delete the edges of subgraph Wm is obtained.Using this method,the vertex distinguishing total chromatic number of K2n＋1／E（Wm） is discussed,and a conjecture of complete graph K2n＋1 delete the edges of subgraph Wm is given,where n≥2 and m≥3.

关 键 词：奇阶完全图 点可区别全染色 点可区别全色数 

分 类 号：O157.5[理学—数学]