Hyper-Wiener Index vs. Wiener Index. Two Highly Correlated Structure-Descriptors

Summary.

 The Wiener (W) and hyper-Wiener (WW) indices of alkanes are found to be highly correlated. Hence, these two structure-descriptors pertain to the very same structural features of the underlying molecules and one of them may be viewed as superfluous. For alkane isomers with n carbon atoms, WW is bounded from both above and below by linear functions of W. The upper bound (n/4+2)W−n(n−1)(n+1)/4 and the lower bound (3/2)W−(n−1)/2 for W≤W ₀ and (3n/4)W−n(n−1)²(n+1) for W≥W ₀, where W ₀=(2/3)(n−1)(n ³−n−1)/(n−2) are better than the previously reported estimates of the same kind. In spite of this, the correlation between W and WW is curvilinear.