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 [Trofimov M. I., "An Optimization of Procedure for Calculation of Hosoya's Index", J. Math. Chem., 1991, 8, 327.] . This graph invariant was introduced by Haruo Hosoya in 1971. [ Hosoya H., Bull. Chem. Soc. Japan, 44, 1971, 2332] . The Hosoya index is often used in chemoinformatics for investigations of organic compounds Hosoya H., " [http://www.biochempress.com/av01_0428.html The Topological Index Z Before and After 1971] ", "Internet Electronic Journal of Molecular Design", 2002, 1, 428–442] [Special issues dedicated to Professor Haruo Hosoya on the occasion of the 65th birthday, Internet Electronic Journal of Molecular Design, [http://www.biochempress.com/cv01_i09.html 2002, vol 1 no. 9] — [http://www.biochempress.com/cv02_i06.html 2003, Volume 2, Number 6] ).]

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the Z index to report a good correlation of the boiling points of alkane isomers and their Z indices, basing on his unpublished 1957 work carried out while he was an undergraduate student at the University of Tokyo..

References

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