{2,3}-Restricted connectivity of locally twisted cubes

Given a graph G and non-negative integer h, the h-restricted connectivity of G is the minimum cardinality of a set of nodes in G, if exists, whose deletion disconnects G and the degree of each node in every remaining component is at least h. The h-restricted connectivity is a generalization of the classical connectivity and can provide more accurate measures for the reliability or fault-tolerance of multiprocessor system. The n-dimensional locally twisted cubes, denoted by LTQn, are a well-known network topology for building multiprocessor systems. In this paper, we first show that 2-restricted connectivity of the n-dimensional locally twisted cubes is 4n−8 for n≥4, and show that 3-restricted connectivity is equal to 8n−24 for n≥5.