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Rainbow connection numbers of Cayley graphs

Author

Listed:
  • Yingbin Ma

    (Henan Normal University
    Nankai University)

  • Zaiping Lu

    (Nankai University)

Abstract

An edge colored graph is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number, rc-number for short, of a graph $${\varGamma }$$ Γ , is the smallest number of colors that are needed in order to make $${\varGamma }$$ Γ rainbow connected. In this paper, we give a method to bound the rc-numbers of graphs with certain structural properties. Using this method, we investigate the rc-numbers of Cayley graphs, especially, those defined on abelian groups and on dihedral groups.

Suggested Citation

  • Yingbin Ma & Zaiping Lu, 2017. "Rainbow connection numbers of Cayley graphs," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 182-193, July.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:1:d:10.1007_s10878-016-0052-6
    DOI: 10.1007/s10878-016-0052-6
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    References listed on IDEAS

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    1. Sourav Chakraborty & Eldar Fischer & Arie Matsliah & Raphael Yuster, 2011. "Hardness and algorithms for rainbow connection," Journal of Combinatorial Optimization, Springer, vol. 21(3), pages 330-347, April.
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    Cited by:

    1. Fu-Hsing Wang & Cheng-Ju Hsu, 2024. "Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids," Mathematics, MDPI, vol. 12(7), pages 1-11, March.
    2. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    3. Ma, Yingbin & Zhu, Wenhan, 2022. "Some results on the 3‐total‐rainbow index," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Nie, Kairui & Ma, Yingbin & Sidorowicz, Elżbieta, 2023. "(Strong) Proper vertex connection of some digraphs," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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    2. Fu-Hsing Wang & Cheng-Ju Hsu, 2024. "Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids," Mathematics, MDPI, vol. 12(7), pages 1-11, March.

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