Abstract
The 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.
The Wiener polarity index Wp of a chemical tree (a graph of a non‐cyclic chemical compound, in which vertices correspond to atoms of the considered compound and the edges correspond to the covalent bonds between atoms), is defined as the number of unordered pairs of its vertices at distance 3. In this article, we characterize the trees having the second maximum Wp value from the class of all chemical trees of a fixed order.