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Group Connectivity in 3-Edge-Connected Graphs

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Abstract

Let A be an abelian group with |A| ≥ 4. For integers k and l with k > 0 and l ≥ 0, let \({{\mathcal C}(k, l)}\) denote the family of 2-edge-connected graphs G such that for each edge cut \({S\subseteq E(G)}\) with two or three edges, each component of G − S has at least (|V(G)| − l)/k vertices. In this paper, we show that if G is 3-edge-connected and \({G\in {\mathcal C}(6,5)}\) , then G is not A-connected if and only if G can be A-reduced to the Petersen graph.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China

    Fan Yang & Xiangwen Li

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  1. Fan Yang
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  2. Xiangwen Li
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Correspondence to Xiangwen Li.

Additional information

X. Li was partially supported by Hubei Key Laboratory of Mathematical Sciences of China.

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Yang, F., Li, X. Group Connectivity in 3-Edge-Connected Graphs. Graphs and Combinatorics 28, 743–750 (2012). https://doi.org/10.1007/s00373-011-1067-5

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  • DOI: https://doi.org/10.1007/s00373-011-1067-5

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