Number of minimum vertex cuts in transitive graphs

Let G be a k-regular vertex transitive graph with connectivity κ(G)=k and let mk(G) be the number of vertex cuts with k vertices. Define m(n,k)=min{mk(G): G∈Tn,k}, where Tn,k denotes the set of all k-regular vertex transitive graphs on n vertices with κ(G)=k. In this paper, we determine the exact values of m(n,k).