, Volume 7, Issue 1, pp 53-64

Eigenvalues, diameter, and mean distance in graphs

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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.

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.