Hamiltonian-Laceability in Star Graphs with Conditional Edge Faults

Abstract

The star graph Sn possess many nice topological properties. It is one of the most versatile and efficient interconnection networks (networks for short) so far discovered for parallel computation. Edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes. It is known that Sn is a bipartite graph. In this paper, we show that for any Sn (n ≥ 4) with ≤ 2n − 7 edge faults in which each node is incident to at least two healthy edges is strongly Hamiltonian laceable. It is also shown that our result is optimal.