Linear Algebra and its Applications 395 (2005) 343–349 www.elsevier.com/locate/laa The spectral radius of trees on k pendant vertices  Baofeng Wu a,b ,∗ , Enli Xiao b , Yuan Hong b a College of Science, Universityof Shanghai for Science and Technology, Shanghai 200093, PR China b Department of Mathematics, East China Normal University, Shanghai 200062, PR China Received 29 January 2002; accepted 26 August 2004 Submitted by R.A. Brualdi Abstract In this paper we consider the following problem: Of all trees of order n with k pendant vertices (n, k fixed), which achieves the maximal spectral radius? We show that the maximal spectral radius is obtained uniquely at T n,k , where T n,k is a tree obtained from a star K 1,k and k paths of almost equal lengths by joining each pendant vertex of K 1,k to an end vertex of one path. We also discuss the spectral radius of T n,k and get some results. © 2004 Elsevier Inc. All rights reserved. AMS classification: 05C50 Keywords: Graph; Tree; Pendant vertex; Spectral radius  Research supported by National Natural Science Foundation of China (No. 19971027) and by Young Scientific Research Fund of USST. ∗ Corresponding author. Address: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China. E-mail addresses: wu_baofeng@yahoo.com.cn (B. Wu), enry2000@163.net (E. Xiao), yhong@math.ecnu.edu.cn (Y. Hong). 0024-3795/$ - see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.laa.2004.08.025