A Bound of Adjacent Vertex-Distinguishing Acyclic Edge Coloring of Graphs
图的邻点可区别无圈边染色的一个界

A proper edge coloring of the 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 to u is not equal to the coloring set of edges incident to v, whereuv\in E(G). In this paper, a new upper bound of adjacent vertex distinguishing acyclic edge coloring of the graph G with no isolated edges is obtained by the way of probability.