Highly Influenced

# Group connectivity of certain graphs

@article{Chen2008GroupCO, title={Group connectivity of certain graphs}, author={Jingjing Chen and Elaine M. Eschen and Hong-Jian Lai}, journal={Ars Comb.}, year={2008}, volume={89} }

- Published 2008 in Ars Comb.

Let G be an undirected graph, A be an (additive) Abelian group and A∗ = A − {0}. A graph G is A-connected if G has an orientation such that for every function b : V (G) 7→ A satisfying ∑ v∈V (G) b(v) = 0, there is a function f : E(G) 7→ A∗ such that at each vertex v ∈ V (G), the net flow out of v equals b(v). We investigate the group connectivity number Λg(G) = min{n : G is A-connected for every Abelian group with |A| ≥ n} for complete bipartite graphs, chordal graphs, and biwheels.