The 3*-connected property of pyramid networks

A k-container C(u, v) of a graph G is a set of k-disjoint paths joining u to v. A k-container C(u, v) of G is a k-container if it contains all the vertices of G. A graph G is k-connected if there exists a k-container between any two distinct vertices in G. Let κ(G) be the connectivity of G. A graph G is superconnected if G is i-connected for all 1 ≤ i ≤ κ(G). The pyramid network is one of the important networks applied in parallel and distributed computer systems. The connectivity of a pyramid network is three. In this paper, we prove that the pyramid network PM[n] is 3-connected and superconnected for n ≥ 1. © 2010 Elsevier Ltd. All rights reserved.