This graph is the unique $\mathrm{SRG}(81,20,1,6)$. It is the coset graph of the truncated ternary Golay code, and the second subconstituent of the point graph of $\mathrm{GQ}(3,9)$.
| Number of vertices: | $81$ |
| Diameter: | $2$ |
| Intersection array: | $\{20,18;1,6\}$ |
| Spectrum: | $20^1 2^{60} (-7)^{20}$ |
| Automorphism group: | $3^4:2. \mathrm{P} \Gamma \mathrm{L}(2,9)$ |
| Distance-transitive: | Yes |
| Primitive |