The h-restricted connectivity of the generalized hypercubes

Abstract

Connectivity is an important index in evaluating the reliability and fault tolerant ability of interconnection network. However the traditional connectivity is inappropriate for large scale multiprocessor systems. The h-restricted connectivity, as a generalization of traditional connectivity, was proposed to estimate the reliability of interconnection networks more accurately. For an interconnection network G and a positive integer h, the cardinality of a vertex subset F is called the h-restricted connectivity of G, denoted κh(G), if F is the minimum vertex set subject to that G−F is disconnected and δ(G−F)≥h. In this paper, we investigate the h-restricted connectivity of the generalized hypercube G(mr,mr−1,…,m1). Specially, we determine that κh(G(mr,mr−1,…,m1))=(h+1)κ(G(mr,mr−1,…,m1))−mmaxh for 1≤h≤min⁡{⌊mr2⌋−1,mmin−1,r}, where κ(G(mr,mr−1,…,m1)) is the connectivity of the generalized hypercube, mmax=max⁡{mr,mr−1,…,m1} and mmin=min⁡{mr,mr−1,…,m1}.