Elliptic semiplanes and regular graphs with girth 5
A (k, g)-graph is a k-regular graph with girth g and a (k, g)-cage is a (k, g)-graph with the fewest possible number of vertices. The cage problem consists of con structing (k, g)-graphs of minimum order n(k, g). We focus on girth g = 5, where cages are known only for degrees k ≤ 7. Considering the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163355 |
| Acceso en línea: | https://hdl.handle.net/11441/163355 https://doi.org/10.1016/j.endm.2018.06.042 |
| Access Level: | acceso abierto |
| Palabra clave: | Regular graphs Girth Cage Amalgam |
| Sumario: | A (k, g)-graph is a k-regular graph with girth g and a (k, g)-cage is a (k, g)-graph with the fewest possible number of vertices. The cage problem consists of con structing (k, g)-graphs of minimum order n(k, g). We focus on girth g = 5, where cages are known only for degrees k ≤ 7. Considering the relationship between fi nite geometries and graphs we establish upper constructive bounds on n(k, 5), for k ∈ {13, 14, 17, 18,.. .} that improve the best so far known. |
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