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Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs. (English) Zbl 1342.90215
Summary: The adjacent vertex-distinguishing chromatic index $$\chi'_{\mathrm{avd}}(G)$$ of a graph $$G$$ is the smallest integer $$k$$ for which $$G$$ admits a proper edge $$k$$-coloring such that no pair of adjacent vertices are incident with the same set of colors. In this paper, we prove that if $$G$$ is a $$2$$-degenerate graph without isolated edges, then $$\chi'_{\mathrm{avd}}(G)\leq\max\{6,\Delta (G)+1\}$$. Moreover, we also show that when $$\Delta\geq 6$$, $$\chi'_{\mathrm{avd}}=\Delta (G)+1$$ if and only if $$G$$ contains two adjacent vertices of maximum degree.

##### MSC:
 90C35 Programming involving graphs or networks 05C15 Coloring of graphs and hypergraphs
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