H-restricted Connectivity of Locally Twisted Cubes

Given a graph G and a non-negative integer h , the h -restricted connectivity of G , denoted by ź h ( G ) , is defined as the minimum size of a set X of nodes in G ( X ź 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 L T Q n , which is a well-known interconnection network for parallel computing, is a variant of the hypercube Q n . 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 ź h ( L T Q n ) = 2 h ( n - h ) for 0 ź h ź n - 2 .