Abstract
The Wiener polarity index (usually denoted by W-p) of an alkane is the number of unordered pairs of carbon atoms which are separated by three carbon-carbon bonds. This topological index W-p is useful for predicting the boiling points of alkanes. Deng [MATCH Commun. Math. Comput. Chem. 66 (2011) 305] proved that the maximum W-p value among all alkanes, with n carbon atoms, is 3n-15. The main purpose of present paper is to find all those alkanes with n carbon atoms, which attain the maximum value of W-p.