The weak $k$-metric dimension of the direct product of complete graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917519789391872 |
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| author | Farhan, Mohammad Kuziak, Dorota Yero, Ismael G. |
| author_facet | Farhan, Mohammad Kuziak, Dorota Yero, Ismael G. |
| contents | The weak $k$-metric dimension of a graph is roughly understood as the cardinality of a smallest set of vertices $S$ of the graph with the property of uniquely recognizing all the vertices of the graph throughout summations of differences of distances to the vertices of $S$. The weak $k$-metric dimension of the direct product of two isomorphic complete graphs is considered in this work. Specifically, the value of such parameter is computed for almost all possibilities of these products and a bound is provided in the remaining case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22307 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The weak $k$-metric dimension of the direct product of complete graphs Farhan, Mohammad Kuziak, Dorota Yero, Ismael G. Combinatorics 05C12, 05C76 The weak $k$-metric dimension of a graph is roughly understood as the cardinality of a smallest set of vertices $S$ of the graph with the property of uniquely recognizing all the vertices of the graph throughout summations of differences of distances to the vertices of $S$. The weak $k$-metric dimension of the direct product of two isomorphic complete graphs is considered in this work. Specifically, the value of such parameter is computed for almost all possibilities of these products and a bound is provided in the remaining case. |
| title | The weak $k$-metric dimension of the direct product of complete graphs |
| topic | Combinatorics 05C12, 05C76 |
| url | https://arxiv.org/abs/2605.22307 |