Group connectivity of certain graphs.
Jingjing Chen, Elaine M. Eschen, Hong‐Jian Lai · 2008
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) ↦ → A satisfying ∑ v∈V (G) b(v) = 0, there is a function f: E(G) ↦ → 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. 1.