Internode Distance and Optimal Routing in a Class of Alternating Group Networks

Alternating group graphs AG_n, studied by Jwo and others, constitute a class of Cayley graphs that possess certain desirable properties compared with other regular networks considered by researchers in parallel and distributed computing. A different form, AN _n, of such graphs, proposed by Youhou and dubbed alternating group networks, has been shown to possess advantages over AG_n. For example, AN_n has a node degree that is smaller by a factor of about 2 while maintaining a diameter comparable to that of AG_n, is maximally fault-tolerant, and shares some of the positive structural attributes of the well-known star graph. In this paper, we characterize the distance between any two nodes in AN_n and present an optimal (shortest-path) routing algorithm for this class of networks