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Eigenvalues, diameter, and mean distance in graphs

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Abstract

It is well-known that the second smallest eigenvalueλ 2 of the difference Laplacian matrix of a graphG is related to the expansion properties ofG. A more detailed analysis of this relation is given. Upper and lower bounds on the diameter and the mean distance inG in terms ofλ 2 are derived.

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Authors and Affiliations

  1. Department of Mathematics, University of Ljubljana, Jadranska 19, 61111, Ljubljana, Yugoslavia

    Bojan Mohar

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  1. Bojan Mohar
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This work was supported in part by the Research Council of Slovenia, Yugoslavia. A part of the work was done while the author was visiting the Ohio State University, supported by a Fulbright grant.

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Mohar, B. Eigenvalues, diameter, and mean distance in graphs. Graphs and Combinatorics 7, 53–64 (1991). https://doi.org/10.1007/BF01789463

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  • DOI: https://doi.org/10.1007/BF01789463

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