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PermuteVertices

  

IsomorphicCopy

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PermuteVertices(G, sigma)

IsomorphicCopy(G, sigma)

Parameters

G

-

graph

sigma

-

(optional) a (permuted) list of the vertices of G

Description

• 

The calling sequence PermuteVertices('G','sigma') returns a new graph H with Vertices(H) = sigma.  The list of neighbors data structure is reordered according to sigma so that the adjacency matrix of H will be different in general.  Attribute information, including vertex position information is also permuted according to sigma so that DrawGraph(H) will look identical to DrawGraph(G).

• 

The calling sequence IsomorphicCopy('G','sigma') returns a new graph H where the list of neighbors data structure is reordered according to sigma but the vertex labels of H are the same as G. It also discards all attributes from G so that if H is drawn, it will not be obvious that H is isomorphic to G.

• 

The calling sequence PermuteVertices('G') chooses a random permutation sigma of the vertices of G then returns H = PermuteVertices(G,sigma). Hence Vertices(H) is the permutation used.

• 

The calling sequence IsomorphicCopy('G') chooses a random permutation sigma of the vertices of G and returns IsomorphicCopy('G','sigma').

Examples

withGraphTheory:

withSpecialGraphs:

GPathGraph5

GGraph 1: an undirected unweighted graph with 5 vertices and 4 edge(s)

(1)

VerticesG,NeighborsG

1,2,3,4,5,2,1,3,2,4,3,5,4

(2)

HPermuteVerticesG,3,5,1,2,4

HGraph 2: an undirected unweighted graph with 5 vertices and 4 edge(s)

(3)

VerticesH

3,5,1,2,4

(4)

NeighborsH

2,4,4,2,3,1,3,5

(5)

HIsomorphicCopyG,3,5,1,2,4

HGraph 3: an undirected unweighted graph with 5 vertices and 4 edge(s)

(6)

VerticesH,NeighborsH

1,2,3,4,5,4,5,5,4,1,3,1,2

(7)

HPermuteVerticesG

HGraph 4: an undirected unweighted graph with 5 vertices and 4 edge(s)

(8)

σVerticesH

σ3,4,5,1,2

(9)

PPrismGraph3,3

PGraph 5: an undirected unweighted graph with 6 vertices and 9 edge(s)

(10)

HIsomorphicCopyP,4,1,2,6,5,3

HGraph 6: an undirected unweighted graph with 6 vertices and 9 edge(s)

(11)

DrawGraphP

DrawGraphH,style=spring

See Also

RelabelVertices

Vertices