On the eigenvalues and spectral radius of starlike trees (Q1662424)

Let \(k\) and \(n_1,\dots,n_k\) be positive integers. In this paper, the eigenvalues are computed for the family of star-like trees \(S(n_1,\dots,n_k)\) that is formed from \(k\) disjoint paths of lenght \(n_1,\dots,n_k\), respectively, each path joined by one leaf to another vertex \(v\). Additionally, the star-like trees whose eigenvalues are in the interval \((-2,2)\) are characterized.