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Rainbow connection numbers of Cayley digraphs on abelian groups

Author

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  • Ma, Yingbin
  • Lu, Zaiping

Abstract

A directed path in an edge colored digraph is said to be a rainbow path if no two edges on this path share the same color. An edge colored digraph Γ is rainbow connected if any two distinct vertices can be reachable from each other through rainbow paths. The rc-number of a digraph Γ is the smallest number of colors that are needed in order to make Γ rainbow connected. In this paper, we investigate the rc-numbers of Cayley digraphs on abelian groups and present an upper bound for such digraphs. In addition, we consider the rc-numbers of bi-Cayley graphs on abelian groups.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:178-183
    DOI: 10.1016/j.amc.2017.05.024
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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).
    2. Ma, Yingbin & Zhu, Wenhan, 2022. "Some results on the 3‐total‐rainbow index," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. 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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