On The Spectral Radius of Trees With Perfect Matchings

Abstract

let G be a simple graph with n venices, We denote λ1(G) the spectral radius of G.in this paper, it is shown that λ1(T)≤λ1(T) and the equatity holds iff .where T is a tree on 2q Vertices with a perfect matching, and T* is a tree from the star K1,q-1, by joining a new end -Vertex to each vertex in K1. q-1.