On the D(β)-vertex-distinguishing acyclic edge chromatic number of graphs
Liu-Xinsheng, Wei-Ziying · 2010
A proper k-edge coloring of a graph G is called D(β)-vertex-distinguishing acyclic edge coloring, if (1) there is no 2-colored cycle in G, and (2) any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the edges incident this vertex. In this paper, we study D(2)-vertex-distinguishing acyclic edge coloring of some special graphs-the cycle Cn, the fan Fn, the wheel Wn, the complete bipartite graph Km, n, and the complete graph Kn. And prove that if G(V, E) is a graph with Δ(G) ≥ 4, and without isolated edges, then X2-vda(G) ≤ 8Δ2.