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Neighbor-distinguishing total coloring of planar graphs with maximum degree twelve

Author

Listed:
  • Jingjing Huo

    (Hebei University of Engineering)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

  • Weifan Wang

    (Zhejiang Normal University)

  • Wenjing Xia

    (Zhejiang Normal University)

Abstract

The neighbor-distinguishing total chromatic number $$\chi ''_{a}(G)$$χa′′(G) of a graph G is the minimum number of colors required for a proper total coloring of G such that any two adjacent vertices have different sets of colors. In this paper, we show that if G is a planar graph with $$\Delta =12$$Δ=12, then $$13\le \chi ''_{a}(G)\le 14$$13≤χa′′(G)≤14, and moreover $$\chi ''_{a}(G)=14$$χa′′(G)=14 if and only if G contains two adjacent 12-vertices.

Suggested Citation

  • Jingjing Huo & Yiqiao Wang & Weifan Wang & Wenjing Xia, 2020. "Neighbor-distinguishing total coloring of planar graphs with maximum degree twelve," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 246-272, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00465-3
    DOI: 10.1007/s10878-019-00465-3
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    References listed on IDEAS

    as
    1. Weifan Wang & Danjun Huang, 2014. "The adjacent vertex distinguishing total coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 379-396, February.
    2. Weifan Wang & Jingjing Huo & Danjun Huang & Yiqiao Wang, 2019. "Planar graphs with $$\Delta =9$$Δ=9 are neighbor-distinguishing totally 12-colorable," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 1071-1089, April.
    3. Xiaohan Cheng & Guanghui Wang & Jianliang Wu, 2017. "The adjacent vertex distinguishing total chromatic numbers of planar graphs with $$\Delta =10$$ Δ = 10," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 383-397, August.
    4. Yang, Donglei & Sun, Lin & Yu, Xiaowei & Wu, Jianliang & Zhou, Shan, 2017. "Neighbor sum distinguishing total chromatic number of planar graphs with maximum degree 10," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 456-468.
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