Edge and mixed metric dimension of Johnson graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910521683345408 |
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| author | Kratica, Jozef Cangalović, Mirjana Kovačević-Vujčić, Vera Danas, Milica Milivojević |
| author_facet | Kratica, Jozef Cangalović, Mirjana Kovačević-Vujčić, Vera Danas, Milica Milivojević |
| contents | In this paper, both edge and mixed metric dimensions of Johnson graphs $J_{n,k}$ are considered. A new tight lower bound for $β_E(J_{n,k})$ based on hitting sets has been obtained. Using this bound, exact values for $β_E(J_{n,2})$ and $β_M(J_{n,2})$ have been derived, and it is proved that $β_E(J_{n,2}) = β_M(J_{n,2})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge and mixed metric dimension of Johnson graphs Kratica, Jozef Cangalović, Mirjana Kovačević-Vujčić, Vera Danas, Milica Milivojević Combinatorics 05C12 G.2.1; G.2.2 In this paper, both edge and mixed metric dimensions of Johnson graphs $J_{n,k}$ are considered. A new tight lower bound for $β_E(J_{n,k})$ based on hitting sets has been obtained. Using this bound, exact values for $β_E(J_{n,2})$ and $β_M(J_{n,2})$ have been derived, and it is proved that $β_E(J_{n,2}) = β_M(J_{n,2})$. |
| title | Edge and mixed metric dimension of Johnson graphs |
| topic | Combinatorics 05C12 G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2407.07851 |