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On the diameter and bisector size of Cayley graphs

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Abstract

We present bounds on two combinatorial properties of Cayley graphs in terms relating to the structure of their underlying group, Included in this work is a presentation of lower bounds on the diameter of Cayley graphs of groups with nilpotent subgroups and upper bounds on the size of node bisectors of Cayley graphs of groups with solvable subgroups.

Cayley graphs, being endowed with algebraic structure, have been increasingly recognized as a source of interconnection networks underlying parallel computers. Their structure has been shown to endow parallel architectures with advantages, for example, in terms of algorithmic efficiency. Our results demonstrate limits on the communication power of certain classes of well-structured interconnection networks.

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Authors and Affiliations

  1. Department of Computer Science, University of Cincinnati, 45221, Cincinnati, OH, USA

    Fred Annexstein

  2. L.R.I., U.A., Université Paris Sud, 410 CNRS, Bât 490, France

    Marc Baumslag

Authors
  1. Fred Annexstein
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  2. Marc Baumslag
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Additional information

A portion of this research was supported by National Science Foundation Grant CCR-88-12567 while both authors were attending the University of Massachusetts.

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Annexstein, F., Baumslag, M. On the diameter and bisector size of Cayley graphs. Math. Systems Theory 26, 271–291 (1993). https://doi.org/10.1007/BF01371728

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  • DOI: https://doi.org/10.1007/BF01371728

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