Cycle Embedding in Alternating Group Graphs with Faulty Elements

Abstract

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. Cycle embedding is an important issue in evaluating the efficiency of interconnection networks. In this paper, we show that an n-dimensional alternating group graph AG n has the following results, where F is the set of faulty vertices and/or faulty edges in AG n : (1) For n ≥ 4, AG n -F is edge 4-pancyclic if |F| ≤ n − 4; and (2) For n ≥ 3, AG n -F is vertex-pancyclic if |F| ≤ n − 3. All the results are optimal with respect to the number of faulty elements tolerated, and they are improvements over the cycle embedding properties of alternating group graphs proposed previously in several articles.