A note on an optimal result on fault-tolerant cycle-embedding in alternating group graphs

In a recently published paper [Z.-J. Xue, S.-Y. Liu, An optimal result on fault-tolerant cycle-embedding in alternating group graphs, Inform. Process. Lett. 109 (21–22) (2009) 1197–1201], the authors showed that for a set of faulty vertices F in an n  -dimensional alternating group graph AGnAGn, AGn−FAGn−F remains pancyclic if |F|≤2n−6|F|≤2n−6. However, the proof of the result is flawed. We will prove the theorem again correcting the defects in the previous proof.

Research highlights
► We show that an AGnAGn remains pancyclic with at most 2n−62n−6 faulty vertices.
► We indicate the defects in the previous proof.
► We prove the theorem again correcting the previous proof.