Eigenvalues, diameter, and mean distance in graphs
Received: 18 June 1988 Revised: 28 November 1989 DOI:
Cite this article as: Mohar, B. Graphs and Combinatorics (1991) 7: 53. doi:10.1007/BF01789463 Abstract
It is well-known that the second smallest eigenvalue
λ 2 of the difference Laplacian matrix of a graph G is related to the expansion properties of G. A more detailed analysis of this relation is given. Upper and lower bounds on the diameter and the mean distance in G in terms of λ 2 are derived.
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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