Generalized nowhere zero flow

Let G be an undirected graph, A be an (additive) abelian group and A* = A - {lcub}0{rcub}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V(G ) A satisfying Sv∈VG b(v) = 0, there is a function f : E(G) A* such that at each vertex v ∈ V(G), ∂f(v), the net flow out from v, equals b( v). An A-nowhere-zero-flow (abbreviated as A-NZF) in G is a function f : E(G) A* such that at each vertex v ∈ V(G), ∂f(v) = 0.;In this paper, we investigate the group connectivity number Lambda g(G) = min{lcub}n : if A is an abelian group with |A| ≥ n, then G is A-connected{rcub} for certain families of graphs including complete bipartite graphs, chordal graphs, wheels and biwheels. We also give some general results and methods to approach nowhere zero flow and group connectivity problems