Desargues graph

Desargues graph
Named after	Gérard Desargues
Vertices	20
Edges	30
Radius	5
Diameter	5
Girth	6
Automorphisms	240 (S5 × S2)
Chromatic number	2
Chromatic index	3
Genus	2
Book thickness	3
Queue number	2
Properties	Cubic Distance-regular Hamiltonian Bipartite Symmetric
Table of graphs and parameters

In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges.^[1] It is named after Girard Desargues, arises from several different combinatorial constructions, has a high level of symmetry, is the only known non-planar cubic partial cube, and has been applied in chemical databases.

The name "Desargues graph" has also been used to refer to a ten-vertex graph, the complement of the Petersen graph, which can also be formed as the bipartite half of the 20-vertex Desargues graph.^[2]