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

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 χAa(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.