Lower Bound for the Spectral Radius of the Starlike Trees

A tree is a connected acyclic graph. A tree is called a starlike if exactly one of its vertices has degree greater than two. Let λ1 be the largest eigenvalue of the adjacency matrix of a starlike tree. In this work, we obtain a lower bound for the spectral radius of a starlike tree. This bound only depends of the maximum degree of the vertices. © 2021 Institute of Physics Publishing. All rights reserved.