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)|o(y) or o(y)|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〉⊂〈y〉 or 〈y〉⊂〈x〉. In this article, we characterize the strong metric dimension of the order supergraph, the enhanced power graph and the reduced power graph of a finite group.

Topics & Concepts