Diameter of 2-distance graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916157001302016 |
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| author | Jafari, S. H. Musawi, S. R. |
| author_facet | Jafari, S. H. Musawi, S. R. |
| contents | For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, for graphs $G$ with diameter 2, we show that $diam(D_2(G))$ can be any integer $t\geqslant2$. For graphs $G$ with $diam(G)\geqslant3$, we prove that $\frac{1}{2}diam(G)\leqslant diam(D_2(G))$ and this inequality is sharp. Also, for $diam(G)=3$, we prove that $diam(D_2(G))\leqslant5$ and this inequality is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diameter of 2-distance graphs Jafari, S. H. Musawi, S. R. Combinatorics For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, for graphs $G$ with diameter 2, we show that $diam(D_2(G))$ can be any integer $t\geqslant2$. For graphs $G$ with $diam(G)\geqslant3$, we prove that $\frac{1}{2}diam(G)\leqslant diam(D_2(G))$ and this inequality is sharp. Also, for $diam(G)=3$, we prove that $diam(D_2(G))\leqslant5$ and this inequality is sharp. |
| title | Diameter of 2-distance graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.07646 |