Hosoya index for an -vertex graph. The number of perfect matchings of the complete graph (with even) is given by the double factorial .

The crossing numbers up to are known, with requiring either 7233 or 7234 crossings. Further values are collected by the Rectilinear Crossing Number project. Rectilinear Crossing numbers for are
:0, 0, 0, 0, 1, 3,