Structural properties of Cayley digraphs with applications to mesh and pruned torus interconnection networks

Authors:
Wenjun Xiao;Behrooz Parhami
Affiliations:
Department of Computer Science, South China University of Technology, Guangzhou 510641, PR China and Department of Mathematics, Xiamen University, Xiamen 361005, PR China;Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Journal of Computer and System Sciences
Year:
2007

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Abstract

Despite numerous interconnection schemes proposed for distributed multicomputing, systematic studies of classes of interprocessor networks, that offer speed-cost tradeoffs over a wide range, have been few and far in between. A notable exception is the study of Cayley graphs that model a wide array of symmetric networks of theoretical and practical interest. Properties established for all, or for certain subclasses of, Cayley graphs are extremely useful in view of their wide applicability. In this paper, we obtain a number of new relationships between Cayley (di)graphs and their subgraphs and coset graphs with respect to subgroups, focusing in particular on homomorphism between them and on relating their internode distances and diameters. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes as well as certain classes of pruned tori.