| Summary: | The hyper-Wiener index WW of a chemical tree T is defined as the sum of the products n1n2, over all pairs u, u of vertices of T, where n1 and n2 are the number of vertices of T, lying on the two sides of the path which connects u and u. We examine a slight modification WWW of the hyper-Wiener index, defined as the sum of the products n1n2n3, over all pairs u, u of vertices of T, where n3 is the number of vertices of T, lying between u and u. It is found that WWW correlates significantly better with various physico-chemical properties of alkanes than WW. Lower and upper bounds for WWW, and an approximate relation between WWW and WW are obtained.
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