Generalized Petersen graph

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GP (n , m )
Elements
Vertices2n 
Edges3n 
Properties
Girthmin(n , 3+m )
Symmetry
Vertex transitiveYes

The generalized Petersen graphs are a family of cubic graphs. The generalized Petersen graph GP (n , m ) is constructed from an outer polygon {n} and an inner polygon {n/m} connecting each vertex in the outer polygon to the corresponding vertex in the inner polygon.

Examples[edit | edit source]

Properties[edit | edit source]

Symmetric generalized Petersen graphs[edit | edit source]

There are exactly seven symmetric generalized Petersen graphs. This set of graphs is exactly the skeleta of the regular polyhedra of type {p,3} with 2p  vertices.[2]

Symemtric generalized Petersen graph
Name Symbol Image Regular polyhedra
P (m ,n ) P (m ,n )π 
Cubical graph GP (4,1) Cube Petrial cube
Petersen graph GP (5,2) Hemidodecahedron
Möbius-Kantor graph GP (8,3) P (8,3) P (8,3)π 
Dodecahedral graph GP (10,2) Dodecahedron Petrial dodecahedron
Desargues graph GP (10,3) P (10,3)
Nauru graph GP (12,5) P (12,5) P (12,5)π 
GP (24,5) P (24,5) P (24,5)π 

External links[edit | edit source]

References[edit | edit source]

Bibliography[edit | edit source]

  • McMullen, Peter (1992), "The regular polyhedra of type {p,3} with 2p  vertices", Geometricae Dedicata, 43 (3), doi:10.1007/BF00151518, ISSN 0046-5755
  • Žitnik, Arjana; Horvat, Boris; Pisanski, Tomaž (2010), All generalized Petersen graphs are unit-distance graphs (PDF), IMFM preprints, 1109