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Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs

Author

Listed:
  • Yi Wang

    (Anhui University)

  • Jian Cheng

    (West Virginia University)

  • Rong Luo

    (West Virginia University)

  • Gregory Mulley

    (West Virginia University)

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.

Suggested Citation

  • Yi Wang & Jian Cheng & Rong Luo & Gregory Mulley, 2016. "Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 874-880, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9796-z
    DOI: 10.1007/s10878-014-9796-z
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    References listed on IDEAS

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    1. Hervé Hocquard & Mickaël Montassier, 2013. "Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 152-160, July.
    2. Weifan Wang & Yiqiao Wang, 2010. "Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 471-485, May.
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    Cited by:

    1. Jingjing Yao & Xiaowei Yu & Guanghui Wang & Changqing Xu, 2017. "Neighbor sum distinguishing total coloring of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 64-70, July.
    2. Xiaolan Hu & Yaojun Chen & Rong Luo & Zhengke Miao, 2017. "Neighbor sum distinguishing index of 2-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 798-809, October.
    3. Junlei Zhu & Yuehua Bu & Yun Dai, 2018. "Upper bounds for adjacent vertex-distinguishing edge coloring," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 454-462, February.

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