Determine isomorphism in the non-normal-subgroup case

Determine whether the derived graphs of voltage graphs whose voltage groups contain non-normal subgroups are isomorphic in cases where the common-cover method does not decide the question.

Background

The paper develops a method for deciding when derived graphs of finite connected voltage graphs are isomorphic. The method constructs a common cover and lifts the voltage assignments; its strongest results apply to Dedekind groups, including abelian groups.

The authors explicitly exhibit a pair of voltage graphs with voltage groups containing non-normal subgroups for which their method does not determine whether the resulting derived graphs are isomorphic. This identifies unresolved instances outside the normal-subgroup setting.

References

However, we provide an example of a pair of voltage graphs, when voltages are taken from groups with subgroups that are not normal, this method does not provide an answer whether corresponding derived graphs are isomorphic.

Lifting Voltages in Graph Covers  (2501.17135 - Jonoska et al., 28 Jan 2025) in Section 1, Introduction