  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($\Delta+2$)/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.
