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Adjacent vertex distinguishing total colorings of outerplanar graphs

Author

Listed:
  • Yiqiao Wang

    (Zhejiang Normal University)

  • Weifan Wang

    (Zhejiang Normal University)

Abstract

An adjacent vertex distinguishing total coloring of a graph G is a proper total 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 total coloring of G is denoted by χ″ a (G). In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of outerplanar graphs.

Suggested Citation

  • Yiqiao Wang & Weifan Wang, 2010. "Adjacent vertex distinguishing total colorings of outerplanar graphs," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 123-133, February.
    • Handle: RePEc:spr:jcomop:v:19:y:2010:i:2:d:10.1007_s10878-008-9165-x
    DOI: 10.1007/s10878-008-9165-x
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    Citations

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    Cited by:

    1. Yulin Chang & Qiancheng Ouyang & Guanghui Wang, 2019. "Adjacent vertex distinguishing total choosability of planar graphs with maximum degree at least 10," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 185-196, July.
    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. Renyu Xu & Jianliang Wu & Jin Xu, 2016. "Neighbor sum distinguishing total coloring of graphs embedded in surfaces of nonnegative Euler characteristic," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1430-1442, May.
    4. 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.
    5. Lin Sun & Xiaohan Cheng & Jianliang Wu, 2017. "The adjacent vertex distinguishing total coloring of planar graphs without adjacent 4-cycles," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 779-790, February.
    6. Xiaohan Cheng & Jianliang Wu, 2018. "The adjacent vertex distinguishing total choosability of planar graphs with maximum degree at least eleven," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 1-13, January.
    7. Hualong Li & Laihao Ding & Bingqiang Liu & Guanghui Wang, 2015. "Neighbor sum distinguishing total colorings of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 675-688, October.
    8. Zengtai Gong & Chen Zhang, 2023. "Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs," Mathematics, MDPI, vol. 11(10), pages 1-25, May.
    9. 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.
    10. Tong Li & Cunquan Qu & Guanghui Wang & Xiaowei Yu, 2017. "Neighbor product distinguishing total colorings," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 237-253, January.

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