On the symmetric division deg index of molecular graphs

The symmetric division deg (SDD) index is one the 148 discrete Adriatic indices, introduced several years ago. The SDD index has already been proved a valuable index in the QSPR/QSAR (quantitative structure-property/activity relationships) studies. In the present paper, we firstly correct an upper bound on the SDD index of molecular trees, reported in the recent paper [MATCH Commun. Math. Comput. Chem. 82 (2019) 43-55], by giving the best possible upper bound on the SDD index of any molecular (n, m)-graph (a molecular graph with order n and size m). We then establish a lower bound on the SDD index of any molecular (n, m)-graph. Finally, by extending a theorem of the aforementioned paper, we characterize the graphs with fifth to ninth minimum SDD indices from the class of all molecular trees having a fixed, but sufficiently large, order.