Pappus graph

The Pappus graph Γ is the bipartite incidence graph of the 9 points and 9 lines of the affine plane AG(2,3) minus a parallel class.

It is cubic, of girth 6. It is the unique distance-regular graph with intersection array {3,2,2,1; 1,1,2,3}.


Γ is distance transitive with group 32:3:2:2:2 of order 216 with point stabilizer D12.


Γ has spectrum ±3, (±√3)6, 04 and is uniquely determined by its spectrum.