New Optimal Results on Codes for Location in Graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916727209590784 |
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| author | Junnila, Ville Laihonen, Tero Lehtilä, Tuomo |
| author_facet | Junnila, Ville Laihonen, Tero Lehtilä, Tuomo |
| contents | In this paper, we broaden the understanding of the recently introduced concepts of solid-locating-dominating and self-locating-dominating codes in various graphs. In particular, we present the optimal, i.e., smallest possible, codes in the infinite triangular and king grids. Furthermore, we give optimal locating-dominating, self-locating-dominating and solid-locating-dominating codes in the direct product $K_n\times K_m$ of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs $K_q\square K_q\square K_q$ with $q\geq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07862 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New Optimal Results on Codes for Location in Graphs Junnila, Ville Laihonen, Tero Lehtilä, Tuomo Discrete Mathematics Combinatorics 05C69, 05C76, 05C63 G.2.2 In this paper, we broaden the understanding of the recently introduced concepts of solid-locating-dominating and self-locating-dominating codes in various graphs. In particular, we present the optimal, i.e., smallest possible, codes in the infinite triangular and king grids. Furthermore, we give optimal locating-dominating, self-locating-dominating and solid-locating-dominating codes in the direct product $K_n\times K_m$ of complete graphs. We also present optimal solid-locating-dominating codes for the Hamming graphs $K_q\square K_q\square K_q$ with $q\geq2$. |
| title | New Optimal Results on Codes for Location in Graphs |
| topic | Discrete Mathematics Combinatorics 05C69, 05C76, 05C63 G.2.2 |
| url | https://arxiv.org/abs/2306.07862 |