The spectral radius of trees on k pendant vertices Original Research Article

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 Tn,k, where Tn,k is a tree obtained from a star K1,k and k paths of almost equal lengths by joining each pendant vertex of K1,k to an end vertex of one path. We also discuss the spectral radius of Tn,k and get some results.