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Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree

Author

Listed:
  • Weifan Wang

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Zhejiang Normal University)

Abstract

An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ′ a (G). Let $\mathop{\mathrm{mad}}(G)$ and Δ denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove the following results: (1) If $\mathop{\mathrm{mad}}(G)

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:19:y:2010:i:4:d:10.1007_s10878-008-9178-5
    DOI: 10.1007/s10878-008-9178-5
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    Citations

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    Cited by:

    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. Chengchao Yan & Danjun Huang & Dong Chen & Weifan Wang, 2014. "Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 893-909, November.
    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. Jingjing Huo & Yiqiao Wang & Weifan Wang, 2017. "Neighbor-sum-distinguishing edge choosability of subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 742-759, October.
    5. Huijuan Wang & Lidong Wu & Weili Wu & Jianliang Wu, 2014. "Minimum number of disjoint linear forests covering a planar graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 274-287, July.
    6. 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.
    7. 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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