Fault-free Hamiltonian Cycles in Alternating Group Graphs with Conditional Edge Faults

The alternating group graph, which belongs to the class of Cayley graphs, is one of the most versatile interconnection networks for parallel and distributed computing. In this paper, adopting the conditional fault model in which each vertex is assumed to be incident with two or more fault-free edges, we show that an n-dimensional alternating group graph can tolerate up to 4n − 13 edge faults, where n ≥ 4, while retaining a fault-free Hamiltonian cycle exists. The result is optimal with respect to the number of edge faults tolerated. Previously, for the same problem, at most 2n – 6 edge faults can be tolerated if the random fault model is adopted.