On the energy of some tree dendrimers
Аннотация
For a graph [Formula: see text] with [Formula: see text] vertices and [Formula: see text] edges, the energy (or the adjacency energy) is the sum of the absolute values of the eigenvalues (or adjacency eigenvalues) of [Formula: see text], that is, [Formula: see text], where [Formula: see text] is the [Formula: see text] adjacency eigenvalue of [Formula: see text]. In this paper, we discuss the characteristic polynomial and the energy of dendrimers. We first show the formula obtained for the characteristic polynomial and the energy of tree dendrimers considered in Bokhary and Tabassum [The energy of some tree dendrimers, J. Appl. Math. Comput. 68 (2022) 1033–1045] are incorrect. Using a different algorithmic procedure we will derive the correct formula for the characteristic polynomial and the energy of dendrimer [Formula: see text]. Further, we obtain the energy of [Formula: see text] for [Formula: see text] and [Formula: see text], which partially answers a problem raised in Bokhary and Tabassum [The energy of some tree dendrimers, J. Appl. Math. Comput. 68 (2022) 1033–1045].