## DIMACS TR: 93-83

## Isoperimetric Inequalities and Eigenvalues

### Author: Nabil Kahale

**
ABSTRACT
**

An upper bound is given on the minimum distance between $i$ subsets
of the same size of a regular graph in terms of the $i$-th largest
eigenvalue in absolute value. This yields a bound on the diameter in
terms of the $i$-th largest eigenvalue, for any integer $i$. Our
bounds are shown to be asymptotically tight. A recent result by
Quenell relating the diameter, the second eigenvalue, and the girth
of a regular graph is obtained as a byproduct.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-83.ps

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