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Cyclic Vertex-Connectivity of Cayley Graphs Generated by Transposition Trees

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Abstract

Let G be a graph. Then \({T\subseteq V(G)}\) is called a cyclic vertex-cut if G − T is disconnected and at least two components in G −T contain a cycle. The cyclic vertex-connectivity is the size of a smallest cyclic vertex-cut. In this paper, we determine this number for Cayley graphs generated by transposition trees as well as classify all the minimum cyclic vertex-cuts.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309, USA

    Eddie Cheng & László Lipták

  2. Department of Computer Science, Brock University, St. Catharines, ON, L2S 3A1, Canada

    Ke Qiu

  3. Department of Computer Science and Technology, Plymouth State University, Plymouth, NH, 03264, USA

    Zhizhang Shen

Authors
  1. Eddie Cheng
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  2. László Lipták
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  3. Ke Qiu
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  4. Zhizhang Shen
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Correspondence to Eddie Cheng.

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Cheng, E., Lipták, L., Qiu, K. et al. Cyclic Vertex-Connectivity of Cayley Graphs Generated by Transposition Trees. Graphs and Combinatorics 29, 835–841 (2013). https://doi.org/10.1007/s00373-012-1172-0

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  • DOI: https://doi.org/10.1007/s00373-012-1172-0

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