2012/08/11 by Lianzhu Zhang, Weifan Wang, Zhang, Lianzhu +3
Mathematics · #05C15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C15
paper · pdf · doi:10.48550/arxiv.1208.2315
arxiv created 2012/08/11 · arxiv updated 2012/08/14
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 χ'a(G). In this paper, we prove that χa'(G) <= 5(Δ+2)/2 for any graph G having maximum degree Δ 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 χa'(G) <= 3Δ for any graph G without isolated edges.