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An Edge-Isoperimetric Problem for Powers of the Petersen Graph

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Abstract.

In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph P n, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of P n are also derived. These results are then generalized for the cartesian product of P n and the m-dimensional binary hypercube.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sicence, University of Visconsin-Superior, Superior, WI 54880, USA, e-mail: sb@math.uwsuper.edu, , , , , , US

    S.L. Bezrukov

  2. Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX 76019-0015, USA, e-mail: das@cse.uta.edu, , , , , , US

    S.K. Das

  3. Department of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, Germany, e-mail: elsa@uni-paderborn.de, , , , , , DE

    R. Elsässer

Authors
  1. S.L. Bezrukov
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  2. S.K. Das
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  3. R. Elsässer
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Received August 20, 1999

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Bezrukov, S., Das, S. & Elsässer, R. An Edge-Isoperimetric Problem for Powers of the Petersen Graph. Annals of Combinatorics 4, 153–169 (2000). https://doi.org/10.1007/s000260050003

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  • DOI: https://doi.org/10.1007/s000260050003

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