Metric and strong metric dimension in commuting graphs of finite groups

ABSTRACT

The commuting graph of a finite group is the undirected graph whose vertex set is the set of all elements of this group, and two distinct vertices are adjacent if they commute. In this paper, we characterize the strong metric dimension of the commuting graph of a finite group and give upper and lower bounds for the metric dimension of the commuting graph of a finite group. As applications, we compute the metric and strong metric dimension of the commuting graph of a dihedral group, a generalized quaternion group and a semidihedral group.

KEYWORDS:

• Commuting graph
• finite group
• metric dimension
• strong metric dimension

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C25
• 05C12

Acknowledgments

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 (Nos. 11801441, 61976244), the National Statistical Science Research Project of China (No. 2022LY096), and the Natural Science Foundation of Shaanxi Province (No 2020JM–425).