The complement of this graph is the Kneser graph $\mathrm{K}(36,2)$.
| Number of vertices: | $630$ |
| Diameter: | $2$ |
| Intersection array: | $\{68,33;1,4\}$ |
| Spectrum: | $68^1 32^{35} (-2)^{594}$ |
| Automorphism group: | $\mathrm{S}_{36}$ |
| Distance-transitive: | Yes |
| Primitive |