Desargues graph

This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
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Definition

The Desargues graph is a particular graph on 20 vertices defined in the following equivalent ways:

1. It is the Levi graph of the Desargues configuration
2. It is the bipartite Kneser graph with parameters 5,2
3. It is the generalized Petersen graph $G(10,3)$.

Arithmetic functions

Size measures

Function	Value	Explanation
size of vertex set	20	As Levi graph of Desargues configuration: number of points + number of lines in the configuration = $10+10=20$ As bipartite Kneser graph with parameters $n=5,k=2$: $2{\binom {n}{k}}=2{\binom {5}{2}}=2(10)=20$ As generalized Petersen graph $G(n,k),n=10,k=3$: $2(10)=20$
size of edge set	30	As Levi graph of Desargues configuration: number of incidences between points and lines = (number of lines) * (number of points on each line) = $(10)(3)=30$ As bipartite Kneser graph with parameters $n=5,k=2$: ${\binom {n}{k,k,n-2k}}={\frac {n!}{k!k!(n-2k)!}}={\binom {5}{2,2,1}}=30$ As generalized Petersen graph $G(n,k),n=10,k=3$: $3n=3(10)=30$