A Fault-Free Unicast Algorithm in the Generalized Hypercube with Restricted Faulty Vertices

Abstract

The generalized hypercube is a highly-connective network proposed by Bhuyan and Agrawal. In this paper, we study the restricted connectivity and fault-free unicast algorithm in the generalized hypercube. Firstly, we prove that the restricted connectivity of a [Formula: see text]-dimensional generalized hypercube [Formula: see text] is [Formula: see text], where [Formula: see text] denotes the connectivity of [Formula: see text] and [Formula: see text] max [Formula: see text], under the condition that each vertex has at least one fault-free neighbor. It is almost twice the traditional connectivity of [Formula: see text]. Furthermore, we present an [Formula: see text] fault-free unicast algorithm in the generalized hypercube.