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Total rainbow connection numbers of some special graphs

Author

Listed:
  • Ma, Yingbin
  • Nie, Kairui
  • Jin, Fengxia
  • Wang, Cui

Abstract

In 2008, Chartrand et al. first introduced the concept of rainbow connection. Since then the study of rainbow connection has received considerable attention in the literature, and now it becomes an active topic in graph theory. As a natural generalization, Uchizawa et al. (2013) and Liu et al. (2014) presented the concept of total rainbow connection, respectively. In this paper, we investigate the total rainbow connection numbers of outerplanar graphs with diameter 2. Applying our result, we improve the main result of [X. Huang, X. Li, Y. Shi, J. Yue, Y. Zhao, Rainbow connections for outerplanar graphs with diameter 2 and 3, Applied Mathematics and Computation, 242(2014), 277–280]. Next, we revise the main result of [Y. Liu, Z. Wang, Rainbow Connection Number of the Thorn Graph, Applied Mathematical Sciences, 8(2014), 6373–6377], and determine the total rainbow connection numbers of graphs G, where G are the thorn graph of complete graph Kn*, the thorn graph of the cycle Cn*. At last, we study the rainbow 2-connection numbers of some special graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:213-220
    DOI: 10.1016/j.amc.2019.05.008
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    References listed on IDEAS

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    1. 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.
    2. Hui Jiang & Xueliang Li & Yingying Zhang, 2016. "Upper bounds for the total rainbow connection of graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 260-266, July.
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    Cited by:

    1. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(C).

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