Graphs and Combinatorics

, Volume 7, Issue 1, pp 53–64

Eigenvalues, diameter, and mean distance in graphs

  • Bojan Mohar

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.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Bojan Mohar
    • 1
  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaYugoslavia