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Structure and pancyclicity of maximal planar graphs with diameter two

Author

Listed:
  • Shu-Yu Cui

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

  • Danjun Huang

    (Zhejiang Normal University)

  • Hongwei Du

    (Harbin Institute of Technology)

  • Weifan Wang

    (Zhejiang Normal University)

Abstract

A graph G on n vertices is called non-universal if its maximum degree is at most $$n-2$$ n - 2 . In this paper, we give a structural characterization for non-universal maximal planar graphs with diameter two. In precise, we find 10 basic graphs, and then generate all 25 non-universal maximal planar graphs with diameter two by adding repeatedly and appropriately 3-vertices to some of these 10 basic graphs. As an application, we show that maximal planar graphs with diameter two are pancyclic except five special graphs.

Suggested Citation

  • Shu-Yu Cui & Yiqiao Wang & Danjun Huang & Hongwei Du & Weifan Wang, 2022. "Structure and pancyclicity of maximal planar graphs with diameter two," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 1-27, January.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00749-7
    DOI: 10.1007/s10878-021-00749-7
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    References listed on IDEAS

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    1. Wang, Yiqiao & Zheng, Lina, 2020. "Computation on the difference of Zagreb indices of maximal planar graphs with diameter two," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Huang, Danjun & Wang, Yiqiao & Lv, Jing & Yang, Yanping & Wang, Weifan, 2019. "List coloring and diagonal coloring for plane graphs of diameter two," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

    1. Kong, Jiangxu & Wang, Yiqiao & Hu, Jiacheng & Wang, Yang & Wang, Weifan, 2023. "Plane graphs of diameter two are 2-optimal," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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