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An Isoperimetric Problem in Cayley Graphs

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Abstract.

Let T be a minimal generating subset of a group G . Let Γ be the Cayley graph defined on G by \(S=T\cup T^{-1}\) . Let d 2 be the minimal cardinality of the boundary of two points. We show that, for |S|>4 , every cutset with cardinality less than d 2 must isolate a single vertex.

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Authors and Affiliations

  1. UFR 921, E. Combinatoire, Universite Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France yha@ccr.jussieu.fr, , , , , , FR

    Y. O. Hamidoune

  2. Dept. Matematica Aplicada i Telematica, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain anna@mat.upc.es, anna@mat.upc.es, , , , , , ES

    A. S. Lladó & O. Serra

Authors
  1. Y. O. Hamidoune
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  2. A. S. Lladó
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  3. O. Serra
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Received April 1996, and in final form February 1999.

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Hamidoune, Y., Lladó, A. & Serra, O. An Isoperimetric Problem in Cayley Graphs . Theory Comput. Systems 32, 507–516 (1999). https://doi.org/10.1007/s002240000129

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  • DOI: https://doi.org/10.1007/s002240000129

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