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...

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Detalles Bibliográficos
Autores: Abajo Casado, María Encarnación, Balbuena, C., Bendala García, Manuel Francisco
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
Descripción
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.