Undirected power graph-equivalent groups
This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.
Definition
Two groups and are termed undirected power graph-equivalent groups if their undirected power graphs are isomorphic as graphs.
Relation with other relations
Stronger relations
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| isomorphic groups | |FULL LIST, MORE INFO | |||
| 1-isomorphic groups | (via directed power graph-equivalent) | (via directed power graph-equivalent) | |FULL LIST, MORE INFO | |
| directed power graph-equivalent groups | |FULL LIST, MORE INFO |