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Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ

Author

Listed:
  • Hervé Hocquard

    (Université Bordeaux I)

  • Mickaël Montassier

    (Université Bordeaux I)

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)

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9444-9
    DOI: 10.1007/s10878-011-9444-9
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    References listed on IDEAS

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    1. 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. Zhuoya Liu & Changqing Xu, 2022. "Adjacent vertex distinguishing edge coloring of IC-planar graphs," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 710-726, May.
    2. 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.
    3. Joanna Skowronek-Kaziów, 2017. "Graphs with multiplicative vertex-coloring 2-edge-weightings," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 333-338, January.
    4. Zengtai Gong & Chen Zhang, 2023. "Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs," Mathematics, MDPI, vol. 11(10), pages 1-25, May.
    5. 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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