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Graphs with (strong) proper connection numbers m−3 and m−4

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  • Ma, Yingbin
  • Zhang, Xiaoxue

Abstract

In 2016, Lumduanhom et al. determined all graphs of size m with PC-number or SPC-number m−1, m−2, m−3. But we find that the graphs with SPC-number m−3 are not completely characterized. In this article, we characterize all graphs with SPC-number m−3. Moreover, we present all graphs satisfying PC-number or SPC-number m−4.

Suggested Citation

  • Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    • Handle: RePEc:eee:apmaco:v:445:y:2023:i:c:s0096300323000127
    DOI: 10.1016/j.amc.2023.127843
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    References listed on IDEAS

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    1. Guan, Xiaxia & Xue, Lina & Cheng, Eddie & Yang, Weihua, 2019. "Minimum degree and size conditions for the proper connection number of graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 205-210.
    2. Hui Lei & Shasha Li & Henry Liu & Yongtang Shi, 2018. "Rainbow vertex connection of digraphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 86-107, January.
    3. Yingbin Ma & Zaiping Lu, 2017. "Rainbow connection numbers of Cayley graphs," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 182-193, July.
    4. Ma, Yingbin & Nie, Kairui & Jin, Fengxia & Wang, Cui, 2019. "Total rainbow connection numbers of some special graphs," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 213-220.
    5. Ma, Yingbin & Lu, Zaiping, 2017. "Rainbow connection numbers of Cayley digraphs on abelian groups," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 178-183.
    Full references (including those not matched with items on IDEAS)

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