On Hamiltonicity and Perfect Codes in Non-Cyclic Graphs of Finite Groups

Parveen Parveen, Bikash Bhattacharjya

Let \( G \) be a finite non-cyclic group. Define \( \mathrm{Cyc}(G) \) as the set of all elements \( a \in G \) such that for any $b\in G$, the subgroup \( \langle a, b \rangle \)…