On the adjacent vertex-distinguishing acyclic edge coloring of some graphs  

作　　者：SHIU Wai Chee CHAN Wai Hong ZHANG Zhong-fu BIAN Liang 

机构地区：[1]（Corresponding author） Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong. [2]Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong. [3]Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第4期439-452,共14页高校应用数学学报（英文版）（B辑）

基　　金：supported by NSFC of China (No. 19871036 and No. 40301037);Faculty Research Grant,Hong Kong Baptist University

摘　　要：A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.

关 键 词：Adjacent strong edge coloring adjacent vertex-distinguishing acyclic edge coloring. 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]