Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five

An adjacent vertex distinguishing edge coloring of a graph (G) is a proper edge coloring of (G) such that any pair of adjacent vertices admit different sets of colors. The minimum number of colors required for such a coloring of (G) is denoted by (chi ^{prime }_{a}(G)) . In this paper, we prove that if (G) is a planar graph with girth at least 5 and (G) is not a 5-cycle, then (chi ^{prime }_{a}(G)le Delta +2) , where (Delta ) is the maximum degree of (G) . This confirms partially a conjecture in Zhang et al. (Appl Math Lett 15:623–626, 2002).