On the inverse eigenvalue problems: the case of superstars

Abstract

Let T be a tree and let x0 be a vertex of T. T is called a superstar with central vertex x₀ if T − x₀ is a union of paths. The General Inverse Eigenvalue Problem for certain trees is partially answered. Using this description, some superstars are presented for which the problem of ordered multiplicity lists and the Inverse Eigenvalue Problem are not equivalent.