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Published in:
01-07-2013
Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ
Published in: Journal of Combinatorial Optimization | Issue 1/2013
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Abstract
An adjacent vertex-distinguishing edge coloring, or avd-coloring, of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let \(\operatorname {mad}(G)\) and Δ(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every graph G with Δ(G)≥5 and \(\operatorname{mad}(G) < 3-\frac {2}{\Delta}\) can be avd-colored with Δ(G)+1 colors. This completes a result of Wang and Wang (J. Comb. Optim. 19:471–485, 2010).