Editing Levi graph (section)

== Examples ==

{{multiple image
 | align = right | perrow = 2 | total_width = 400
 | image1 = Fano plane-Levi graph.svg
 | image2 = Fano plane with nimber labels.svg
 | footer = Heawood graph and Fano plane<br><small>Vertex <span style="background-color: #eee; border: 1px solid #ddd;">3</span> is part of the circular edge <span style="background-color: #eee; border: 1px solid #ddd; white-space: nowrap;">(3, 5, 6)</span>, the diagonal edge <span style="background-color: #eee; border: 1px solid #ddd; white-space: nowrap;">(3, 7, 4)</span>, and the side edge <span style="background-color: #eee; border: 1px solid #ddd; white-space: nowrap;">(1, 3, 2)</span>.</small>
}}
* The [[Desargues graph]] is the Levi graph of the [[Desargues configuration]], composed of 10 points and  10 lines. There are 3 points on each line, and 3 lines passing through each point. The Desargues graph can also be viewed as the [[generalized Petersen graph]] G(10,3) or the [[Kneser graph|bipartite Kneser graph]] with parameters 5,2. It is 3-regular with 20 vertices.
* The [[Heawood graph]] is the Levi graph of the [[Fano plane]]. It is also known as the (3,6)-[[cage (graph theory)|cage]], and is 3-regular with 14 vertices.
* The [[Möbius–Kantor graph]] is the Levi graph of the [[Möbius–Kantor configuration]], a system of 8 points and 8 lines that cannot be realized by straight lines in the Euclidean plane. It is 3-regular with 16 vertices.
* The [[Pappus graph]] is the Levi graph of the [[Pappus configuration]], composed of 9 points and 9 lines. Like the Desargues configuration there are 3 points on each line and 3 lines passing through each point. It is 3-regular with 18 vertices.
* The [[Gray graph]] is the Levi graph of a configuration that can be realized in <math>\R^3</math> as a <math>3\times 3\times 3</math> grid of 27 points and the 27 orthogonal lines through them.
* The [[Tutte eight-cage]] is the Levi graph of the [[Cremona–Richmond configuration]]. It is also known as the (3,8)-cage, and is 3-regular with 30 vertices.
* The four-dimensional [[hypercube graph]] <math>Q_4</math> is the Levi graph of the [[Möbius configuration]] formed by the points and planes of two mutually incident tetrahedra.
* The [[Ljubljana graph]] on 112 vertices is the Levi graph of the Ljubljana configuration.<ref name="LUB">{{cite report
 | last1 = Conder | first1 = Marston |author1-link=Marston Conder
 | last2 = Malnič | first2 = Aleksander
 | last3 = Marušič | first3 = Dragan |author3-link=Dragan Marušič
 | last4 = Pisanski | first4 = Tomaž | author4-link = Tomaž Pisanski
 | last5 = Potočnik | first5 = Primož
 | publisher = University of Ljubljana Department of Mathematics
 | type = IMFM Preprint | volume = 40-845
 | title = The Ljubljana Graph
 | url = http://www.imfm.si/preprinti/PDF/00845.pdf
 | year = 2002}}.</ref>