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Isoperimetric numbers of graph bundles

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Abstract

The main aim of this paper is to give some upper and lower bounds for the isoperimetric numbers of graph coverings or graph bundles, with exact values in some special cases. In addition, we show that the isoperimetric number of any covering graph is not greater than that of the base graph. Mohar's theorem for the isoperimetric number of the cartesian product of a graph and a complete graph can be extended to a more general case: The isoperimetric numberi(G × K 2n) of the cartesian product of any graphG and a complete graphK 2n on even vertices is the minimum of the isoperimetric numberi(G) andn, and it is also a sharp lower bound of the isoperimetric numbers of all graph bundles over the graphG with fiberK 2n. Furthermore, ifn ≥ 2i(G) then the isoperimetric number of any graph bundle overG with fibreK n is equal to the isoperimetric numberi(G) ofG.

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Authors and Affiliations

  1. Mathematics, Pohang University of Science and Technology, 790-784, Pohang, Korea

    Jin Ho Kwak

  2. Mathematics, Yeungnam University, 712-749, Kyongsan, Korea

    Jaeun Lee

  3. Mathematics, Changwon National University, 641-240, Changwon, Korea

    Moo Young Sohn

Authors
  1. Jin Ho Kwak
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  2. Jaeun Lee
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  3. Moo Young Sohn
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Partially supported by The Ministry of Education, Korea.

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Kwak, J.H., Lee, J. & Sohn, M.Y. Isoperimetric numbers of graph bundles. Graphs and Combinatorics 12, 239–251 (1996). https://doi.org/10.1007/BF01858458

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  • DOI: https://doi.org/10.1007/BF01858458

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