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GraphTheory[SpecialGraphs]

  

GeneralizedPetersenGraph

  

construct generalized Petersen graph

 

Calling Sequence

Parameters

Description

Examples

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

withGraphTheory:

withSpecialGraphs:

PGeneralizedPetersenGraph5,2

P:=Graph 1: an undirected unweighted graph with 10 vertices and 15 edge(s)

(1)

DrawGraphP

PGeneralizedPetersenGraph6,2

P:=Graph 2: an undirected unweighted graph with 12 vertices and 18 edge(s)

(2)

DrawGraphP

See Also

PetersenGraph

SpecialGraphs

 


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