Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs

Yi Wang (), Jian Cheng (), Rong Luo () and Gregory Mulley ()
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Yi Wang: Anhui University
Jian Cheng: West Virginia University
Rong Luo: West Virginia University
Gregory Mulley: West Virginia University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 26, 874-880

Abstract: Abstract The adjacent vertex-distinguishing chromatic index $$\chi '_{avd}(G)$$ χ a v d ′ ( G ) of a graph $$G$$ G is the smallest integer $$k$$ k for which $$G$$ G admits a proper edge $$k$$ k -coloring such that no pair of adjacent vertices are incident with the same set of colors. In this paper, we prove that if $$G$$ G is a $$2$$ 2 -degenerate graph without isolated edges, then $$\chi '_{avd} (G)\le \max \{6, \Delta (G)+1\}$$ χ a v d ′ ( G ) ≤ max { 6 , Δ ( G ) + 1 } . Moreover, we also show that when $$\Delta \ge 6$$ Δ ≥ 6 , $$\chi '_{avd}= \Delta (G)+1$$ χ a v d ′ = Δ ( G ) + 1 if and only if $$G$$ G contains two adjacent vertices of maximum degree.

Keywords: Adjacent vertex-distinguishing edge coloring; $$2$$ 2 -Degenerate; Maximum degree (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9796-z

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