Group Connectivity of Kneser Graphs

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 D(G) 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 ∑e∈E+(v) f(e) − ∑ e∈E−(v) f(e) = b(v). For an abelian group A, let 〈A〉 be the family of graphs that are A-connected. The group connectivity number Λg(G) = min{n : if A is an abelian group with |A| ≥ n, then G ∈ 〈A〉}. Let [n] = {1, 2, · · · , n}, and ( X k ) represents the set of all k-subsets of X. For n > 2k, the Kneser graph KG(n, k) has vertex set: ( [n] k ) , edge set: A ∼ B if and only if A⋂B = ∅. In this paper, the group connectivity of Kneser graph are determined or given its limits. Mathematics Subject Classification: 022