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 ? 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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