Further mathematical properties of Cayley digraphs applied to hexagonal and honeycomb meshes

Authors:
Wenjun Xiao;Behrooz Parhami
Affiliations:
Department of Computer Science, South China University of Technology, Guangzhou 510641, China;Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

In this paper, we extend known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups to obtain a number of general results on homomorphism between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes, including the derivation of provably correct shortest-path routing algorithms for such networks.