Editing Petersen graph (section)

== Constructions ==
[[File:Kneser graph KG(5,2).svg|class=skin-invert-image|thumb|left|Petersen graph as Kneser graph <math>KG_{5,2}</math>]]
The Petersen graph is the [[complement graph|complement]] of the [[line graph]] of <math>K_5</math>. It is also the [[Kneser graph]] <math>KG_{5,2}</math>; this means that it has one vertex for each 2-element [[subset]] of a 5-element set, and two vertices are connected by an edge if and only if the corresponding 2-element subsets are disjoint from each other. As a Kneser graph of the form <math>KG_{2n-1,n-1}</math> it is an example of an [[odd graph]].

Geometrically, the Petersen graph is the graph formed by the vertices and edges of the [[hemi-dodecahedron]], that is, a [[dodecahedron]] with opposite points, lines and faces identified together.