Some results on symmetric double starlike trees

Abstract

A tree is called starlike if it has exactly one vertex of degree greater than two. In [2] it was proved that two starlike trees are cospectral if and only if they are isomorphic. A tree is called double starlike if it has exactly two adjacent vertices of degree greater than two. We prove here that there exist no two cospectral non-isomorphic symmetric double starlike trees.