Abstract
Using eigenvalue interlacing and Chebyshev polynomials we find upper bounds for the diameter of regular and bipartite biregular graphs in terms of their eigenvalues. This improves results of Chung and Delorme and Solé. The same method gives upper bounds for the number of vertices at a given minimum distance from a given vertex set. These results have some applications to the covering radius of error-correcting codes.
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