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arXiv · 2412.20558

On some metric properties of supertoken graphs

E. T. Baskoro·C. Dalfó·M. A. Fiol·R. Simanjuntak
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Abstract

In this paper, we construct two infinite families of graphs $G(d,c)$ and $G^+(d,c)$, where, in both cases, a vertex label is $x_1x_2\ldots x_c$ with $x_i\in\{1,2,\ldots, d\}$. We provide a lower bound on the metric dimension, tight on $G^+(d,c)$. Moreover, we give the definition and properties of the supertoken graphs, a generalization of the well-known token graphs. Finally, we provide an upper bound on the metric dimension of supertoken graphs.

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E. T. Baskoro, C. Dalfó, M. A. Fiol, R. Simanjuntak. 2024-12-29. On some metric properties of supertoken graphs. https://arxiv.org/abs/2412.20558

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