Strong metric dimensions for power graphs of finite groups

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 $⟨x⟩\subset ⟨y⟩$ or $⟨y⟩\subset ⟨x⟩$. 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.

This is the final version to be published in Communications in Algebra, 16 pages

References in corpus (3)

• The power graph of a torsion-free group
• The Cyclic Graph of a Z-group
• Some results on the reduced power graph of a group