New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be constructed using a generalization to Zn of the concept of congruence in Z. Here w...

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Detalles Bibliográficos
Autores: Dalfó, Cristina, Fiol Mora, Miguel Ángel, López Lorenzo, Ignacio
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/69200
Acceso en línea:https://doi.org/10.1007/s00026-020-00496-2
http://hdl.handle.net/10459.1/69200
Access Level:acceso abierto
Palabra clave:Mixed graph
Moore bound
Abelian group
Congruences in Zn
Descripción
Sumario:Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be constructed using a generalization to Zn of the concept of congruence in Z. Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.