Spectral Radius and maximum degree of connected graphs

2006/02/01 by Vladimir Nikiforov, Nikiforov, Vladimir
Mathematics · Computer Science · Engineering · #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.math/0602028

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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