Super Spanning Connectivity of Augmented Cubes

Abstract

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 nodes of G. A graph G is k*-connected if there exists a k*-container between any two distinct nodes. The spanning connectivity of G, kappa* (G), is defined to be the largest integer k such that G is omega*-connected for all 1 <= omega <= k if G is an 1*-connected graph and undefined if otherwise. A graph G is super spanning connected if kappa*(G) = kappa(G). In this paper, we prove that the n-dimensional augmented cube AQ(n) is super spanning connected.