A note on the alternating group network
The class of alternating group networks was introduced in the late 1990's as an alternative to the alternating group graphs as interconnection networks. Recently, additional properties for the alternating group networks have been published. In particular, Zhou et al., J. Supercomput (2009), doi: 10.1007/s11227-009-0304-7, was published very recently in this journal. We show that this so-called new interconnection topology is in fact isomorphic to the (n, n - 2)- star, a member of the well-known (n, k)-stars, 1 <= k <= n - 1, a class of popular networks proposed earlier for which a large amount of work have already been done. Specifically, the problem in Zhou et al., J. Supercomput (2009), doi: 10.1007/s11227-009-0304-7, was addressed in Lin and Duh, Inf. Sci. 178(3), 788-801, 2008, when k = n-2.
alternating group network isomorphism (n, k)-star graph