An upper bound for the vertex-distinguishing acyclic edge chromatic number of graphs
Wei Zi-ying · Journal of Lanzhou University · 2010
If a proper edge coloring f of graph G satisfies:1) there is no 2-colored cycle in G;2) for any two distinct vertices u and v of V(G),we have C(u)≠C(v),where C(u) ={f(uw) | uw∈E(G)},then f is called a vertex-distinguishing acyclic edge coloring of graph G.The vertex-distinguishing acyclic edge chromatic number of G,denoted byχ′_(vda)(G) is the minimal number of colors in a vertex-distinguishing acyclic edge coloring of G.It was proved that if G(V,E) is a graph withδ≥5,and n≤30Δ~4,thenχ′_(vda)(G)≤10Δ~2,where n is the order of G andδ(G) the minimum degree of G,andΔ(G) the maximum degree of G.