Editing Petersen graph (section)

==Related graphs==
[[File:Petersen family.svg|class=skin-invert-image|thumb|The [[Petersen family]].]]
The [[generalized Petersen graph]] <math>G(n,k)</math> is formed by connecting the vertices of a [[regular polygon|regular ''n''-gon]] to the corresponding vertices of a [[star polygon]] with [[Schläfli symbol]] {''n''/''k''}.<ref>{{citation | author-link = Harold Scott MacDonald Coxeter
 | first = H. S. M. | last = Coxeter
 | title = Self-dual configurations and regular graphs
 | journal = [[Bulletin of the American Mathematical Society]]
 | volume = 56 | year = 1950 | pages = 413–455
 | doi = 10.1090/S0002-9904-1950-09407-5
 | issue = 5| doi-access = free
 }}.
</ref><ref>{{Citation | first=Mark E.|last=Watkins | title=A Theorem on Tait Colorings with an Application to the Generalized Petersen Graphs | journal=[[Journal of Combinatorial Theory]] | year=1969 | volume=6 | pages=152&ndash;164 | doi=10.1016/S0021-9800(69)80116-X | issue=2| doi-access=free }}</ref> For instance, in this notation, the Petersen graph is <math>G(5,2)</math>: it can be formed by connecting corresponding vertices of a pentagon and five-point star, and the edges in the star connect every second vertex. The generalized Petersen graphs also include the ''n''-prism <math>G(n,1)</math> the [[Dürer graph]] <math>G(6,2)</math>, the [[Möbius-Kantor graph]] <math>G(8,3)</math>, the [[dodecahedron]] <math>G(10,2)</math>, the [[Desargues graph]] <math>G(10,3)</math> and the [[Nauru graph]] <math>G(12,5)</math>.

The [[Petersen family]] consists of the seven graphs that can be formed from the Petersen graph by zero or more applications of [[Y-Δ transform|Δ-Y or Y-Δ transform]]s. The [[complete graph]] ''K''<sub>6</sub> is also in the Petersen family. These graphs form the [[forbidden minor]]s for [[linkless embedding|linklessly embeddable graphs]], graphs that can be embedded into three-dimensional space in such a way that no two cycles in the graph are [[Link (knot theory)|linked]].<ref name=Bailey1997>{{Citation|title=Surveys in Combinatorics|page=187|last1=Bailey|first1=Rosemary A.| publisher= Cambridge University Press|year=1997|isbn=978-0-521-59840-8}}</ref>

The [[Clebsch graph]] contains many copies of the Petersen graph as [[induced subgraph]]s: for each vertex ''v'' of the Clebsch graph, the ten non-neighbors of ''v'' induce a copy of the Petersen graph.

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