Desargues graph

Desargues graph
Named afterGérard Desargues
Vertices20
Edges30
Radius5
Diameter5
Girth6
Automorphisms240 (S5 × S2)
Chromatic number2
Chromatic index3
Genus2
Book thickness3
Queue number2
PropertiesCubic
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]

  1. ^ Weisstein, Eric W., "Desargues Graph", MathWorld
  2. ^ Kagno, I. N. (1947), "Desargues' and Pappus' graphs and their groups", American Journal of Mathematics, 69 (4), The Johns Hopkins University Press: 859–863, doi:10.2307/2371806, JSTOR 2371806.