Fault-Free Ring Embedding in Faulty Wrapped Butterfly Graphs

Abstract

In this paper, we study cycle embedding in a faulty wrapped butterfly BFn with at most two faults in vertices and/or edges. Let F be a subset of V (BFn)∪E(BFn) with |F| ≤ 2. Let fv denote |F ∩ V (BFn)|. In this paper, we prove that BFn−F contains a cycle of length n×2n−2fv. Moreover, BFn − F contains a cycle of length n × 2n − fv if n is an odd integer. In other words, BFn − F contains a hamiltonian cycle if n is an odd integer.