Edge-fault-tolerant pancyclicity of 2-tree-generated networks

Jwo et al. introduced the alternating group graph as an interconnection network topology for computing systems. A graph is pancyclic if it contains cycles of all possible lengths. P-Y Tsai et al. showed that the alternating group graph AG_n is pancyclic, and remains pancyclic after the deletion of 2n−6 edges. In this paper we consider a class of Cayley graphs introduced by Cheng et al. that are generated by certain 3-cycles on the alternating group (Formula presented.). These graphs are generalizations of the alternating group graph AG_n. We look at the case when the 3-cycles form a ‘tree-like structure’, and analyse the pancyclicity of these graphs. We prove that this family of Cayley graphs is (2n-6)-edge-fault-tolerant pancyclic.