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A kind of conditional connectivity of Cayley graphs generated by wheel graphs

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  • Tu, Jianhua
  • Zhou, Yukang
  • Su, Guifu

Abstract

For a connected graph G=(V,E), a subset F ⊆ V is called an Rk-vertex-cut of G if G−F is disconnected and each vertex in V−F has at least k neighbors in G−F. The cardinality of the minimum Rk-vertex-cut is the Rk-vertex-connectivity of G and is denoted by κk(G). The conditional connectivity is a measure to explore the structure of networks beyond the vertex-connectivity. Let Sym(n) be the symmetric group on {1,2,…,n} and T be a set of transpositions of Sym(n). Denote by G(T) the graph with vertex set {1,2,…,n} and edge set {ij:(ij)∈T}. If G(T) is a wheel graph, then simply denote the Cayley graph Cay(Sym(n),T) by WGn. In this paper, we determine the values of κ1 and κ2 for Cayley graphs generated by wheel graphs and prove that κ1(WGn)=4n−6 and κ2(WGn)=8n−18.

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  • Tu, Jianhua & Zhou, Yukang & Su, Guifu, 2017. "A kind of conditional connectivity of Cayley graphs generated by wheel graphs," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 177-186.
    • Handle: RePEc:eee:apmaco:v:301:y:2017:i:c:p:177-186
    DOI: 10.1016/j.amc.2016.12.015
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    Cited by:

    1. Hu, Xiaomin & Tian, Yingzhi & Meng, Jixiang, 2018. "Super Rk-vertex-connectedness," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 812-819.
    2. Wei, Yulong & Xu, Min, 2018. "The 1, 2-good-neighbor conditional diagnosabilities of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 295-310.
    3. Yu Yang & Long Li & Wenhu Wang & Hua Wang, 2020. "On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs," Mathematics, MDPI, vol. 9(1), pages 1-29, December.

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