Equidistant dimension of Johnson and Kneser 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_ | 1866917943543070720 |
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| author | Kratica, Jozef Čangalović, Mirjana Kovačević-Vujčić, Vera |
| author_facet | Kratica, Jozef Čangalović, Mirjana Kovačević-Vujčić, Vera |
| contents | In this paper the recently introduced concept of equidistant dimension $eqdim(G)$ of graph $G$ is considered. Useful property of distance-equalizer set of arbitrary graph $G$ has been established. For Johnson graphs $J_{n,2}$ and Kneser graphs $K_{n,2}$ exact values for $eqdim(J_{n,2})$ and $eqdim(K_{n,2})$ have been derived, while for Johnson graphs $J_{n,3}$ it is proved that $eqdim(J_{n,3}) \le n-2$. Finally, exact value of $eqdim(J_{2k,k})$ for odd $k$ has been presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17870 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equidistant dimension of Johnson and Kneser graphs Kratica, Jozef Čangalović, Mirjana Kovačević-Vujčić, Vera Combinatorics 05C12 G.2.2 In this paper the recently introduced concept of equidistant dimension $eqdim(G)$ of graph $G$ is considered. Useful property of distance-equalizer set of arbitrary graph $G$ has been established. For Johnson graphs $J_{n,2}$ and Kneser graphs $K_{n,2}$ exact values for $eqdim(J_{n,2})$ and $eqdim(K_{n,2})$ have been derived, while for Johnson graphs $J_{n,3}$ it is proved that $eqdim(J_{n,3}) \le n-2$. Finally, exact value of $eqdim(J_{2k,k})$ for odd $k$ has been presented. |
| title | Equidistant dimension of Johnson and Kneser graphs |
| topic | Combinatorics 05C12 G.2.2 |
| url | https://arxiv.org/abs/2406.17870 |