On power graphs of finite groups with forbidden induced subgraphs

Abstract

The power graph $\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\in ⟨y⟩$ or $y\in ⟨x⟩$. We characterize all finite groups $G$ whose power graphs are claw-free, $K_{1,4}$-free or $C_4$-free.

9 pages, To appear in Indag. Math