On the second maximum Wiener polarity index of chemical trees of a fixed order

Abstract

AbstractThe Wiener polarity index Wp of a graph is defined as the number of unordered pairs of its vertices at distance 3. The problem of finding trees attaining the maximum Wp value, among all chemical trees of a fixed order n, was solved in the paper (Mol. Inf. 2019, 38, 1800076) for n ≥ 8. Motivated by the usage of Wp in a recent publication (J. Chem. Inf. Model. 2020, 60, 1224–1234), in this article we extend the work done in the aforementioned paper by giving a further ordering of chemical trees with respect to the maximum value of Wp. More precisely, we characterize the trees having the second maximum Wp value (which is 3n − 16) from the class of all chemical trees of a fixed order n, for n ≥ 9.