Abstract
Let $G$ be a finite group. The reduced power graph of $G$ is the undirected graph whose vertex set is $G$, and two distinct vertices $x$ and $y$ are adjacent if $\langle x \rangle \subset \langle y \rangle$ or $\langle y \rangle \subset \langle x \rangle$. In this paper, we give tight upper and lower bounds for the metric dimension of the reduced power graph of a finite group. As applications, we compute the metric dimension of the reduced power graph of a $\mathcal{P}$-group, a cyclic group, a dihedral group, a generalized quaternion group, and a group of odd order.
Funding Statement
This research was supported by the National Natural Science
Foundation of China (Grant No. 11801441), the Natural Science Basic Research Program of Shaanxi
(Program Nos. 2020JQ-761 and 2021JM-399), and the Young Talent fund of University Association
for Science and Technology in Shaanxi, China (Grant No. 20190507).
Acknowledgments
We are grateful to the referees for many detailed comments and thoughtful suggestions that have helped improve this paper substantially.
Citation
Xuanlong Ma. Lan Li. "On the Metric Dimension of the Reduced Power Graph of a Finite Group." Taiwanese J. Math. 26 (1) 1 - 15, February, 2022. https://doi.org/10.11650/tjm/210905
Information