The [formula omitted]-restricted connectivity of balanced hypercubes

Abstract

Restricted connectivity is a measure of fault-tolerance in multiprocessing systems. The h-restricted connectivity of a graph G, denoted by κh(G), is the minimum cardinality of vertex set F such that G−F is disconnected and the degree of each component is at least h. In this paper, we study the h-restricted connectivity of n-dimensional balanced hypercube BHn and prove that κ2h(BHn)=κ2h−1(BHn)=4h(n−h), where 1≤h≤⌊n2⌋ and n≥2.