On extremal (almost) edge-girth-regular 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_ | 1866916108456427520 |
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| author | Araujo-Pardo, Gabriela Kiss, György Porupsánszki, István |
| author_facet | Araujo-Pardo, Gabriela Kiss, György Porupsánszki, István |
| contents | A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $λ$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, λ)$ if has the smallest possible order. We prove that some graphs arising from incidence graphs of finite planes are extremal egr-graphs. We also prove new lower bounds on the order of egr-graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On extremal (almost) edge-girth-regular graphs Araujo-Pardo, Gabriela Kiss, György Porupsánszki, István Combinatorics 05C35, 51E12, 51E15 A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $λ$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, λ)$ if has the smallest possible order. We prove that some graphs arising from incidence graphs of finite planes are extremal egr-graphs. We also prove new lower bounds on the order of egr-graphs. |
| title | On extremal (almost) edge-girth-regular graphs |
| topic | Combinatorics 05C35, 51E12, 51E15 |
| url | https://arxiv.org/abs/2401.15411 |