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Internode Distance and Optimal Routing in a Class of Alternating Group Networks
December 2006 (vol. 55 no. 12)
pp. 1645-1648
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.

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Index Terms:
Alternating group graph, Cayley graph, diameter, interconnection network, internode distance, optimal routing, permutation group, regular graph, shortest-path routing.
Citation:
Baoxing Chen, Wenjun Xiao, Behrooz Parhami, "Internode Distance and Optimal Routing in a Class of Alternating Group Networks," IEEE Transactions on Computers, vol. 55, no. 12, pp. 1645-1648, Dec. 2006, doi:10.1109/TC.2006.199
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