Small regular graphs of girth 7
In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of mi...
| Autores: | , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/86686 |
| Acesso em linha: | https://hdl.handle.net/2117/86686 |
| Access Level: | acceso abierto |
| Palavra-chave: | Combinatorial analysis Directed graphs Cages Girth Incidence graph Bipartite graphs Construction Anàlisi combinatòria Grafs dirigits Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Resumo: | In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7 and order 2q(3) + q(2) + 2q for each even prime power q >= 4, and of order 2q(3) + 2q(2) q + 1 for each odd prime power q >= 5. |
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