A tree distinguishing polynomial

Abstract We define a bivariate polynomial for unlabeled rooted trees and show that the polynomial of an unlabeled rooted tree T is the generating function of a class of subtrees of T . We prove that the polynomial is a complete isomorphism invariant for unlabeled rooted trees. Then, we generalize the polynomial to unlabeled unrooted trees and we show that the generalized polynomial is a complete isomorphism invariant for unlabeled unrooted trees.