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]
^Weisstein, Eric W., "Desargues Graph", MathWorld
^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.
field of graph theory, the Desarguesgraph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after Girard Desargues, arises...
projective geometry. Desargues' theorem, the Desarguesgraph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a...
after Girard Desargues. The Desargues configuration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in...
10 , 2 ) {\displaystyle G(10,2)} , the Desarguesgraph G ( 10 , 3 ) {\displaystyle G(10,3)} and the Nauru graph G ( 12 , 5 ) {\displaystyle G(12,5)} ....
space. For every Levi graph, there is an equivalent hypergraph, and vice versa. The Desarguesgraph is the Levi graph of the Desargues configuration, composed...
Petersen graphs are the n-prism G(n, 1), the Dürer graph G(6, 2), the Möbius-Kantor graph G(8, 3), the dodecahedron G(10, 2), the Desarguesgraph G(10, 3)...
3-regular graphs. Every strongly regular graph is symmetric, but not vice versa. Heawood graph Möbius–Kantor graph Pappus graphDesarguesgraph Nauru graph Coxeter...
graph, the Desarguesgraph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T....
vertices. The bipartite Kneser graph H(5, 2) is the Desarguesgraph and the bipartite Kneser graph H(n, 1) is a crown graph. Watkins (1970). Lovász (1978)...
In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning...
In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of...
is the Desarguesgraph: K2 × G(5,2) = G(10,3). The bipartite double cover of a complete graph Kn is a crown graph (a complete bipartite graph Kn,n minus...
graph is the Desarguesgraph: K2 × G(5,2) = G(10,3). The bipartite double cover of a complete graph Kn is a crown graph (a complete bipartite graph Kn...
Nauru graph and the Desarguesgraph are integral. The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande...
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color...
resulting graph is a bipartite Kneser graph; the graph formed in this way with n = 2 has 20 vertices and 30 edges, and is called the Desarguesgraph. All median...
various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...
{\displaystyle G(10,2)} and the Desarguesgraph G ( 10 , 3 ) {\displaystyle G(10,3)} . The Nauru graph is a Cayley graph of S4, the symmetric group of permutations...
Thesis, University of Tübingen, 2018 Kagno, I. N. (1947), "Desargues' and Pappus' graphs and their groups", American Journal of Mathematics, 69 (4),...
projective spaces; such embeddability is a consequence of a property known as Desargues' theorem, not shared by all projective planes. A projective plane consists...
graph and the Desarguesgraph. Any hypercube graph, such as the four-dimensional hypercube shown below, is also bivariegated. However, the graph shown below...
plane, even though the plane is too small to contain a non-degenerate Desargues configuration (which requires 10 points and 10 lines). The lines of the...
In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert...
Global Information