Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model

Abstract

A graph G is said to be conditional k-edge-fault pancyclic if after removing k faulty edges from G, under the assumption that each node is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to $|V(G)|$. In this paper, we consider the common properties of a wide class of interconnection networks, called restricted hypercube-like networks, from which their conditional edge-fault pancyclicity can be determined. We then apply our technical theorems to show that several multiprocessor systems, including n-dimensional locally twisted cubes, n-dimensional generalized twisted cubes, recursive circulants $G(2^{n},4)$ for odd n, n-dimensional crossed cubes, and n-dimensional twisted cubes for odd n, are all conditional $(2n-5)$-edge-fault pancyclic.