An improved upper bound on the adjacent vertex distinguishing chromatic index of a graph

Institute of Mathematics, Academia Sinica; NSFC [11171279, 10831001, 11071223, 11371328]; NSC [99-2115-M-001-004-MY3]An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident with distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing coloring of G is denoted by chi(a)'(G). In this paper, we prove that chi(a)'(G) <= 5/2(Delta + 2) for any graph G having maximum degree Delta and no isolated edges. This improves a result in [S. Akbari, H. Bidkhori, N. Nosrati, r-strong edge colorings of graphs, Discrete Math. 306 (2006)3005-3010], which states that chi(a)'(G) <= 3 Delta for any graph G without isolated edges. (C) 2013 Elsevier B.V. All rights reserved