Some facts are-
Group can be represented by a graph.
Group Isomorphism $\leq_p$ Graph Isomorphism.
Under this context, my questions is-
- Can a triangle free graph represent a group?
Edit: My motivation is to see the interaction between group isomorphism and graph isomorphism,so please consider groups that can be represented by simple graphs but not trees as tree isomorphism can be solved in log time.
In general, consider hard instances of groups for group isomorphism which are represented by graphs that are also hard graph isomorphism instances.