最大度为6的图的邻点可区别边色数  

Adjacent Vertex Distinguishing Index of Graphs with Maximum Degree Six

作　　者：霍京京 王艺桥[2] HUO JINGJING;WANG YIQIAO(Department of Mathematics,Hebei University of Engineering,Handan 056038,China;School of Management,Beijing University of Chinese Medicine,Beijing 100029,China)

机构地区：[1]河北工程大学数理科学与工程学院,邯郸056038 [2]北京中医药大学管理学院,北京100029

出　　处：《应用数学学报》2018年第6期788-800,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11701136,11671053,11501161);河北省自然科学基金(A2016402164)资助项目

摘　　要：图G的邻点可区别边染色是G的一个正常边染色,使得每一对相邻顶点有不同的颜色集合.图G的邻点可区别边色数χ′α(G)是使得G有邻点可区别边染色的最少颜色数.本文证明了:若G是一个最大度为6的图,则χ′α(G)≤12.A proper edge coloring of a graph G is called adjacent vertex distinguishing,if any pair of adjacent vertices have distinct color sets. The adjacent vertex distinguishing index of G, denoted by X′α(G),is the smallest integer k such that G has an adjacent vertex distinguishing edge k-coloring. In this paper, we show that every graph G with maximum degree △=6 and without isolated edges has X′α(G)≤ 12.

关 键 词：邻点可区别边染色 最大度 边分解 

分 类 号：O157.5[理学—数学]