This graph is the unique rank-3 $\mathrm{SRG}(135,70,37,35)$. It is the first subconstituent of the $\mathrm{VO}_8^+(2)$ graph. The complement of this graph is the unique rank-3 $\mathrm{SRG}(135,64,28,32)$.
| Number of vertices: | $135$ |
| Diameter: | $2$ |
| Intersection array: | $\{70,32;1,35\}$ |
| Spectrum: | $70^1 7^{50} (-5)^{84}$ |
| Automorphism group: | $\mathrm{PSO}^+(8,2)$ |
| Distance-transitive: | Yes |
| Primitive |