GeneralizedPetersenGraph - Maple Help

GraphTheory[SpecialGraphs]

 GeneralizedPetersenGraph
 construct generalized Petersen graph

 Calling Sequence GeneralizedPetersenGraph(n, k)

Parameters

 n - positive integer >=3 k - positive integer

Description

 • The GeneralizedPetersenGraph(n,k) command returns the generalized Petersen graph with the given parameters.
 • If n and k are relatively prime, the graph consists of two cycles of length n with a perfect matching between their vertices. The i'th vertex of the first cycle is connected to the ki'th vertex on the second cycle.
 • If n and k are not relatively prime, the graph consists of one cycle of length n perfectly matched to another set of n vertices forming gcd(k,n) cycles of length n/gcd(k,n).

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $P≔\mathrm{GeneralizedPetersenGraph}\left(5,2\right)$
 ${P}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 10 vertices and 15 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(P\right)$
 > $P≔\mathrm{GeneralizedPetersenGraph}\left(6,2\right)$
 ${P}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 12 vertices and 18 edge\left(s\right)}}$ (2)
 > $\mathrm{DrawGraph}\left(P\right)$