Finite groups with star-free noncyclic graphs

Xuanlong Ma, Gary L. Walls, Kaishun Wang

For a finite noncyclic group $G$, let $\Cyc(G)$ be a set of elements $a$ of $G$ such that $⟨a,b⟩$ is cyclic for each $b$ of $G$. The noncyclic graph of $G$ is a graph…