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I am trying to produce Cayley graphs for finite groups defined using presentations, but I am getting strange results.

For example, the following should produce the Cayley graph for the cyclic group with 3 elements:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
C = G.cayley_graph()
C.plot()

but the graph produced has 4 vertices (sorry I can't upload an image).

If I tell Sage the list of elements like so:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
L = G.list()
C = G.cayley_graph(elements = L,generators = [x,x^-1])
C.plot()

then the number of vertices is correct, but there are no edges between $x$ and $x^{-1}(=x^2)$.

Does anyone know how to fix this?

I am trying to produce Cayley graphs for finite groups defined using presentations, presentations, but I am getting strange results.

For example, the following should produce the Cayley graph for the cyclic group with 3 elements:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
C = G.cayley_graph()
C.plot()

but the graph produced has 4 vertices (sorry I can't upload an image).5 vertices:

If I tell Sage the list of elements like so:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
L = G.list()
C = G.cayley_graph(elements = L,generators = [x,x^-1])
G.cayley_graph(elements=L, generators=[x, x^-1])
C.plot()

then the number of vertices is correct, but there are no edges between $x$ and $x^{-1}(=x^2)$.$x^{-1}(=x^2)$:

Does anyone know how to fix this?

I am trying to produce Cayley graphs for finite groups defined using presentations, but I am getting strange results.

For example, the following should produce the Cayley graph for the cyclic group with 3 elements:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
C = G.cayley_graph()
C.plot()

but the graph produced has 5 vertices:

If I tell Sage the list of elements like so:

F.<x> = FreeGroup()
rel = [ x^3 ]
G = F/rel
L = G.list()
C = G.cayley_graph(elements=L, generators=[x, x^-1])
C.plot()

then the number of vertices is correct, but there are no edges between $x$ and $x^{-1}(=x^2)$:

Does anyone know how to fix this?