Desargues graph: Difference between revisions

Revision as of 22:14, 29 May 2012

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:

It is the Levi graph of the Desargues configuration
It is the bipartite Kneser graph with parameters 5,2
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 $G(n,k),n=10,k=3$ : $2(10)=20$

@@ Line 8: / Line 8: @@
 # It is the [[defining ingredient::bipartite Kneser graph]] with parameters 5,2
 # It is the [[defining ingredient::generalized Petersen graph]] <math>G(10,3)</math>.
+==Arithmetic functions==
+===Size measures===
+{| class="sortable" border="1"
+! Function !! Value !! Explanation
+|-
+| {{arithmetic function value|size of vertex set|20}} || As Levi graph of Desargues configuration: number of points + number of lines in the configuration = <math>10 + 10 = 20</math><br>As bipartite Kneser graph with parameters <math>n = 5, k = 2</math>: <math>2 \binom{n}{k} = 2 \binom{5}{2} = 2(10) = 20</math><br>As generalized Petersen graph <math>G(n,k), n = 10, k = 3</math>: <math>2(10) = 20</math>
+|}