Fault-tolerant edge and vertex pancyclicity in alternating group graphs

In J.-M. Chang, J.-S. Yang. Fault-tolerant cycle-embedding in alternating group graphs, Appl. Math. Comput. 197 (2008) 760-767] the authors claim that every alternating group graph AG_n is (n − 4)-fault-tolerant edge 4-pancyclic. Which means that if the number of faults ∣F∣ ? n − 4, then every edge in AG_n − F is contained in a cycle of length ?, for every 4 ? ? ? n!/2 − ∣F∣. They also claim that AG_n is (n − 3)-fault-tolerant vertex pancyclic. Which means that if ∣F∣ ? n − 3, then every vertex in AG_n − F is contained in a cycle of length ?, for every 3 ? ? ? n!/2 − ∣F∣. Their proofs are not complete. They left a few important things unexplained. In this paper we fulfill these gaps and present another proofs that AG_n is (n − 4)-fault-tolerant edge 4-pancyclic and (n − 3)-fault-tolerant vertex pancyclic.