Formula omitted]-restricted connectivity of locally twisted cubes

Abstract

Given a graph G and a non-negative integer h, the h-restricted connectivity of G, denoted by κh(G), is defined as the minimum size of a set X of nodes in G (X⊂V(G)) such that G−X is disconnected, and the degree of each component in G−X is at least h. The h-restricted connectivity measure is a generalization of the traditional connectivity measure, and it improves the connectivity measurement accuracy. Moreover, studies have revealed that if a network possesses a restricted connectivity property, it is more reliable and demonstrates a lower node failure rate compared with other networks. The n-dimensional locally twisted cube LTQn, which is a well-known interconnection network for parallel computing, is a variant of the hypercube Qn. Most studies have examined the h-restricted connectivity of networks under the conditions of h=1 or h=2. This paper examines a generalized h-restricted connectivity measure for n-dimensional locally twisted cube and reveals that κh(LTQn)=2h(n−h) for 0≤h≤n−2.