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).

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$P≔\mathrm{GeneralizedPetersenGraph}\left(5\,2\right)$

$P≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{DrawGraph}\left(P\right)$

$P≔\mathrm{GeneralizedPetersenGraph}\left(6\,2\right)$

$P≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 18\; edge(s)}$

$\mathrm{DrawGraph}\left(P\right)$