On bipartite biregular large graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910401559527424 |
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| author | Araujo-Pardo, G. Dalfó, C. Fiol, M. A. López, N. |
| author_facet | Araujo-Pardo, G. Dalfó, C. Fiol, M. A. López, N. |
| contents | A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter $d=3$ and asymptotically optimal order for given degrees $r$ and $s$. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On bipartite biregular large graphs Araujo-Pardo, G. Dalfó, C. Fiol, M. A. López, N. Combinatorics A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter $d=3$ and asymptotically optimal order for given degrees $r$ and $s$. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound. |
| title | On bipartite biregular large graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.04680 |