Desargues graph

There is a unique distance-regular graph with intersection array {3,2,2,1,1;1,1,2,2,3}. It has 20 vertices and spectrum 31 24 15 (-1)5 (-2)4 (-3)1. It is the bipartite double of the Petersen graph.

The name is derived from Desargues' theorem, that describes a configuration of 10 points and 10 lines. The Desargues graph is the bipartite point-line incidence graph of that configuration.

This configuration is found as the configuration of 10 internal points and 10 elliptic lines for a conic in PG(2,5).