Finding Optimal Routings in Hamming Graphs |
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Authors: | Tian Khoon Lim Cheryl E Praeger |
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Institution: | Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiaf1 |
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Abstract: | A routing R in a graph consists of a simple path puvfromu to v for each ordered pair of distinct vertices (u, v). We will call R optimal if all the paths puvare shortest paths and if edges of the graph occur equally often in the paths of R. In 1994, Solé gave a sufficient condition involving the automorphism group for a graph to have an optimal routing in this sense. Graphs which satisfy Solé’s condition are called orbital regular graphs. It is often difficult to determine whether or not a given graph is orbital regular. In this paper, we give a necessary and sufficient condition for a Hamming graph to be orbital regular with respect to a certain natural subgroup of automorphisms. |
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