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 $〈x〉\subset 〈y〉$ or $〈y〉\subset 〈x〉.$ 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.

Keywords:

• Enhanced power graph
• finite group
• order supergraph
• reduced power graph
• strong metric dimension

2020 Mathematics Subject Classification:

• 05C25
• 05C69

Acknowledgment

We are grateful to the anonymous referee for careful reading and helpful comments.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11801441 and 61976244), the Natural Science Basic Research Program of Shaanxi (Program No. 2020JQ-761), and the Young Talent fund of University Association for Science and Technology in Shaanxi, China (Grant No. 20190507).