# Constructing Cayley Graphs

I am having confusions in constructing a Cayley Graph in Sage Math. Say, I want to construct the Cayley graph on the Symmetric Group $S_4$ with respect to the generating set consisting of all transpositions, what code do I use.

I tried the following minimal code:

```
G = SymmetricGroup(4)
CG = G.cayley_graph(generators=[PermutationGroupElement([1, 2]),
PermutationGroupElement([1, 3]),
PermutationGroupElement([1, 4]),
PermutationGroupElement([2, 3]),
PermutationGroupElement([2, 4]),
PermutationGroupElement([3, 4])])
CGU = CG.to_undirected()
CGU.show()
```

But, I get the error

```
501 # a valid permutation (else segfaults, infinite loops may occur).
502 if not is_valid_permutation(self.perm, self.n):
--> 503 raise ValueError("invalid data to initialize a permutation")
504
505 # This is more expensive
ValueError: invalid data to initialize a permutation
```

How do I rectify the code so as to produce my desired Cayley Graph. Any suggestions?