Graph invariants | Matching (graph theory) | Mathematical chemistry
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. The index is named after Haruo Hosoya. It is used as a topological index in chemical graph theory. Complete graphs have the largest Hosoya index for any given number of vertices; their Hosoya indices are the telephone numbers. (Wikipedia).
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