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 ...
