Group Connectivity of Bridged Graphs |
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Authors: | Liangchen Li Xiangwen Li Chi Shu |
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Affiliation: | 1. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China
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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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