Strong metric dimensions for power graphs of finite groups (2005.03829v2)

Abstract: Let $G$ be a finite group. The order supergraph of $G$ is the graph with vertex set $G$, and two distinct vertices $x,y$ are adjacent if $o(x)\mid o(y)$ or $o(y)\mid o(x)$. The enhanced power graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices are adjacent if they generate a cyclic subgroup. The reduced power graph of $G$ is the graph with vertex set $G$, and two distinct vertices $x,y$ are adjacent if $\langle x\rangle \subset \langle y\rangle$ or $\langle y\rangle \subset \langle x\rangle$. In this paper, we characterize the strong metric dimension of the order supergraph, the enhanced power graph and the reduced power graph of a finite group.