Spanning Connectivity of the WK-Recursive Networks

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k∗-container if it contains all vertices of G. A graph G is k∗connected if there exists a k∗-container between any two distinct vertices. The spanning connectivity of G, κ∗(G), is defined to be the largest integer k such that G is w∗-connected for all 1 ≤ w ≤ k if G is an 1∗-connected graph and undefined if otherwise. We use K(d, t) to denote the WK-recursive network of level t, each of which basic modules is a d-vertex complete graph, where d > 1 and t ≥ 1. In this paper, we prove that the κ∗(K(d, t)) = d−1 for d ≥ 4 and t ≥ 1.