Graphs and Combinatorics

, Volume 7, Issue 1, pp 53–64

Eigenvalues, diameter, and mean distance in graphs


  • Bojan Mohar
    • Department of MathematicsUniversity of Ljubljana

DOI: 10.1007/BF01789463

Cite this article as:
Mohar, B. Graphs and Combinatorics (1991) 7: 53. doi:10.1007/BF01789463


It is well-known that the second smallest eigenvalueλ2 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 ofλ2 are derived.

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© Springer-Verlag 1991