On minimal energies of trees with given diameter

Abstract

The energy of G, denoted by E(G), is defined as the sum of the absolute values of the eigenvalues of G. In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a conjecture proposed by B. Zhou and F. Li [J. Math. Chem., 39:465-473, 2006] is completely solved.