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Maximum Degree Condition and Group Connectivity

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Abstract

Let A be an abelian group with \({|A|\geq 4}\). Suppose that G is a 3-edge-connected simple graph on \({n\geq 19}\) vertices. It is proved in this paper that if \({\max\{d(u), d(\upsilon)\}\geq \frac{n}{6}}\) for every pair of nonadjacent vertices u and υ, then G is A-connected, which generalizes the early result by Yao et al. (Discrete Mathematics 310:1050–1058, 2010).

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Authors and Affiliations

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

    Xiaoxia Zhang & Xiangwen Li

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  1. Xiaoxia Zhang
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  2. Xiangwen Li
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Correspondence to Xiangwen Li.

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Supported by National Science Foundation of China Research Grant (11171129).

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Zhang, X., Li, X. Maximum Degree Condition and Group Connectivity. Graphs and Combinatorics 30, 1055–1063 (2014). https://doi.org/10.1007/s00373-013-1315-y

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  • DOI: https://doi.org/10.1007/s00373-013-1315-y

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