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Constructing graphs using permutation or symmetric groups

asked 2019-05-04 22:47:42 +0100

homiermorphism gravatar image

updated 2019-08-29 18:19:40 +0100

FrédéricC gravatar image

I'm trying to construct a graph whose vertices are the elements of a permutation group or a symmetric group. Whenever I do this, it ignores the identity element (). For instance, when I use the Symmetric Group S3, it prints a graph with 5 vertices and the missing vertex is the identity.

Any ideas on why this happening and how I can fix it?

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Welcome to Ask Sage! Thank you for your question.

slelievre gravatar imageslelievre ( 2019-05-05 11:18:02 +0100 )edit

Please provide some code to let others reproduce the problem easily.

This dramatically increases the chances of an answer, the speed of getting an answer, and the accuracy with which the answers target the problem.

slelievre gravatar imageslelievre ( 2019-05-05 11:18:52 +0100 )edit

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answered 2019-05-05 11:27:55 +0100

slelievre gravatar image

Using the Graph([list_of_vertices, list_of_edges]) construction, one can build a graph with vertices the elements in the symmetric group $S_3$, and with no edges, as follows:

sage: S = SymmetricGroup(3)
sage: G = Graph([list(S), []])
sage: G
Graph on 6 vertices

Not a very interesting graph... If the goal is a Cayley graph, use the dedicated method:

sage: C = S.cayley_graph()
sage: C
Digraph on 6 vertices

Tested with SageMath 8.8.beta4 built for Python 3.

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Asked: 2019-05-04 22:47:42 +0100

Seen: 382 times

Last updated: May 05 '19