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On the Spectrum, the Growth, and the Diameter of a Graph

✍ Scribed by N. Hajaj

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
171 KB
Volume
76
Category
Article
ISSN
0095-8956

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✦ Synopsis

A lower bound is given for the harmonic mean of the growth in a finite undirected graph 1 in terms of the eigenvalues of the Laplacian of 1. For a connected graph, this bound is tight if and only if the graph is distance-regular. Bounds on the diameter of a ``sphere-regular'' graph follow. Finally, a lower bound is given for the growth in an infinite undirected graph of bounded degree in terms of the spectrum of its Laplacian.

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