Spectral radius and degree sequence of a graph

Abstract

Let G be a simple connected graph of order n with degree sequence d(1), d(2), ... , dr, in non-increasing, order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer l at most n, we give a sharp upper bound for rho(G) by a function of d(1), d(2), ... ,d(l), which generalizes a series of previous results. (C) 2013 Elsevier Inc. All rights reserved.