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Spectral Radius and maximum degree of connected graphs

Vladimir Nikiforov
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Abstract

We give an upper bound on the maximal eigenvalue of the adjacency matrix of a connected graph in terms of its maximum degree, diameter and order. This bound is best possible up to a constant factor and improves prevoius results of Stevanovic, Zhang, and Alon and Sudakov.

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Vladimir Nikiforov. 2006-02-01. Spectral Radius and maximum degree of connected graphs. https://arxiv.org/abs/math/0602028

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