On the spectral radius of trees

Abstract In this paper, we investigated the spectral radius of trees and obtained the following result: Let T be a tree on n vertices. Let M(T) denote one maximum matching of T and |M(T)|=i . Let T i * be a tree as shown in Fig. 1. Then ρ(T)⩽ 1 2 (n−i+1+ (n−i+1) 2 −4(n−2i+1) ) , and equality holds if and only if T=T i * .