# Constructing graphs using permutation or symmetric groups 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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Please provide some code to let others reproduce the problem easily.

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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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