In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, and in drug design since they can be correlated with a large number of physico-chemical properties of molecules. As the main result, we de...

The ap index (and derived indices) can be recalibrated by using Mayaud's am index to recover the correct universal time variations. Such variations were artificially removed in the original ap index. A number of tests are performed to show that the corrected index is capable of revealing •he desired variations. These tests include comparisons of the universal time variations on days of opposite...

BACKGROUND Bipolar disorder (BD) is a serious and recurring condition that affects approximately 2.4% of the global population. About half of BD sufferers have an illness course characterized by either a manic or a depressive predominance. This predominant polarity in BD may be differentially associated with several clinical correlates. The concept of a polarity index (PI) has been recently pro...

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also ...

Among various topological indices considered in chemical graph theory, only a few have been widely studied in mathematical and chemical literatures. However, it seems that less attention has been paid to the Wiener polarity index. It was introduced by Harold Wiener1 for acyclic molecules in 1947. The Wiener polarity index of an organic molecule the molecular graph of which is G = (V,E) is defin...

Reversed-phase high-performance liquid chromatography (RP-HPLC) has been carried out for a series of unsubstituted polycyclic aromatic hydrocarbons (PAHs) and the corresponding ethynyl, 1,3-butadiynyl, and 1,3,5-hexatriynyl derivatives. Theoretical values of the isotropic polarizability and several polarity descriptors have been computed for each compound by using semiempirical models and densi...