SUPER SPANNING CONNECTIVITY OF THE FULLY CONNECTED CUBIC NETWORKS

Abstract

A k-containerC(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 a 1*-connected graph and undefined otherwise. A graph G is super spanning connected if κ* (G) = κ(G). In this paper, we prove that the n-dimensional fully connected cubic network FCCNn is super spanning connected.