Hosoya index

The Hosoya index, also known as the topological index or Z index of a graph is the total number of matchings in it plus 1 ("plus 1" accounts for the number of matchings with 0 edges). Its computational complexity is O(exp(E)), where E is number of edges^[1]. This graph invariant was introduced by Haruo Hosoya in 1971.^[2]. The Hosoya index is often used in chemoinformatics for investigations of organic compounds ^{[3] [4]}

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In his article "The Topological Index Z Before and After 1971" on the history of the notion and the associated inside stories, Horoya writes that he introduced the Z index to report a good correlation of the boiling points of alkane isomers and their Z indices, basing on his unpublished 1957 work carried out while he was an undergraduate student at the University of Tokyo.^[3].

References

1. ^ Trofimov M. I., An Optimization of Procedure for Calculation of Hosoya's Index, J. Math. Chem., 1991, 8, 327.
2. ^ Hosoya H., Bull. Chem. Soc. Japan, 44, 1971, 2332
3. ^ ^{a b} Hosoya H., The Topological Index Z Before and After 1971, Internet Electronic Journal of Molecular Design, 2002, 1, 428–442
4. ^ Special issues dedicated to Professor Haruo Hosoya on the occasion of the 65th birthday, Internet Electronic Journal of Molecular Design, 2002, vol 1 no. 9 — 2003, Volume 2, Number 6).

• Roberto Todeschini, Viviana Consonni (2000) "Handbook of Molecular Descriptors", Wiley-VCH, ISBN 3527299130