Abstract Let I(G; x) denote the independence polynomial of a graph G. Alavi, Malde, Schwenk and Erdős conjectured for any tree T that I(T; x) is unimodal. In this paper, we derive that rooted products of some trees preserve real-rootedness of independence polynomials. In consequence, we obtain more and more trees whose independence polynomials have only real zeros. This in particular implies that their independence polynomials are unimodal. This is a preview of subscription content, to check access.
