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Hosoya index : ウィキペディア英語版 | Hosoya index
The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. ==History== This graph invariant was introduced by Haruo Hosoya in 1971.〔.〕 It is often used in chemoinformatics for investigations of organic compounds.〔.〕〔(Internet Electronic Journal of Molecular Design ), special issues dedicated to Professor Haruo Hosoya on the occasion of the 65th birthday: Volume 1 (2002), Number 9 — Volume 2 (2003), 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the Z index to report a good correlation of the boiling points of alkane isomers and their Z indices, basing on his unpublished 1957 work carried out while he was an undergraduate student at the University of Tokyo.〔
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