Group connectivity for Km,n-k - Zhang, Yue; Yin, Jian-Hua (Utilitas Mathematica, 2013)
Let G be an undirected graph, A be an (additive) abelian group with identity 0, 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 Sigma;vεV(G) b( v) = 0, there is a function f : E(G) → A* such that at each vertex v ε V(G), the net flow out of v equals b(v). For a graph G, the group connectivity number of G is defined as follows: Λg(G) = minh|G is A-connected for every abelian group A with |A| ≥ h. In this paper, we determine the value of Λg(Km, n-k) for m ≥ n ≥ 3 except for the graph K5,4-4, where Km,n-k is the graph obtained from the m × n complete bipartite graph Km,n by removing k independent edges.