On some metric properties of supertoken graphs
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910766383235072 |
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| author | Baskoro, E. T. Dalfó, C. Fiol, M. A. Simanjuntak, R. |
| author_facet | Baskoro, E. T. Dalfó, C. Fiol, M. A. Simanjuntak, R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some metric properties of supertoken graphs Baskoro, E. T. Dalfó, C. Fiol, M. A. Simanjuntak, R. Combinatorics 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. |
| title | On some metric properties of supertoken graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.20558 |