Steps To Reproduce

Each element of automorphism group acts on the graph vertices by permuting (relabeling) them. It is therefore very natural for .relabel() to support automorphism group's elements.

sage: G = graphs.CycleGraph(5)
sage: A = G.automorphism_group()
sage: H = G.random_orientation()
sage: a = A.random_element()
sage: print(a)
(0,3,1,4,2)
sage: H.relabel(a,inplace=False).show()

Expected Behavior

For a given automorphism a, each graph vertex v should be relabeled into a(v).

Actual Behavior

At the moment .relabel() misunderstands a given graph's automorphism by issuing an wrongful error message NotImplementedError: Non injective relabeling. Elements of automorphism group do define injective labeling.

Additional Information

A workaround is to call H.relabel(lambda v: a(v),...) instead of H.relabel(a,...).

Environment

- **OS**: Ubuntu 22.04.3 LTS
- **Sage Version**: 10.3.beta7

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide