Given a finite group $ G $ with the identity $ e $, the TI-power graph (trivial intersection power graph) of $ G $ is an undirected graph with vertex set $ G $, in which two distinct vertices $ x $ and $ y $ are adjacent if $ \langle x\rangle\cap \langle y\rangle = \{e\} $. In this paper, we obtain closed formulas for the metric and strong metric dimensions of the TI-power graph of a finite group. As applications, we compute the metric and strong metric dimensions of the TI-power graph of a cyclic group, a dihedral group, a generalized quaternion group, and a semi-dihedral group.
Citation: Chunqiang Cui, Jin Chen, Shixun Lin. Metric and strong metric dimension in TI-power graphs of finite groups[J]. AIMS Mathematics, 2025, 10(1): 705-720. doi: 10.3934/math.2025032
Given a finite group $ G $ with the identity $ e $, the TI-power graph (trivial intersection power graph) of $ G $ is an undirected graph with vertex set $ G $, in which two distinct vertices $ x $ and $ y $ are adjacent if $ \langle x\rangle\cap \langle y\rangle = \{e\} $. In this paper, we obtain closed formulas for the metric and strong metric dimensions of the TI-power graph of a finite group. As applications, we compute the metric and strong metric dimensions of the TI-power graph of a cyclic group, a dihedral group, a generalized quaternion group, and a semi-dihedral group.
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Chunqiang Cui, Jin Chen, Shixun Lin. Metric and strong metric dimension in TI-power graphs of finite groups[J]. AIMS Mathematics, 2025, 10(1): 705-720. doi: 10.3934/math.2025032
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