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Group Connectivity of Bridged Graphs

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Abstract

Let G be a 2-edge-connected simple graph, and let A denote an abelian group with the identity element 0. If a graph G * is obtained by repeatedly contracting nontrivial A-connected subgraphs of G until no such a subgraph left, we say G can be A-reduced to G*. A graph G is bridged if every cycle of length at least 4 has two vertices x, y such that d G (x, y) < d C (x, y). In this paper, we investigate the group connectivity number Λ g (G) = min{n: G is A-connected for every abelian group with |A| ≥ n} for bridged graphs. Our results extend the early theorems for chordal graphs by Lai (Graphs Comb 16:165–176, 2000) and Chen et al. (Ars Comb 88:217–227, 2008).

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Authors and Affiliations

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

    Liangchen Li, Xiangwen Li & Chi Shu

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  1. Liangchen Li
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  2. Xiangwen Li
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  3. Chi Shu
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Corresponding author

Correspondence to Xiangwen Li.

Additional information

X. Li was supported by the Natural Science Foundation of China (11171129).

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Li, L., Li, X. & Shu, C. Group Connectivity of Bridged Graphs. Graphs and Combinatorics 29, 1059–1066 (2013). https://doi.org/10.1007/s00373-012-1154-2

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  • DOI: https://doi.org/10.1007/s00373-012-1154-2

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