A survey on the missing Moore graph

This is a survey on some known properties of the possible Moore graph (or graphs) ϒ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ϒ induced by a vertex subset C, the following graphs are distance-regular:...

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Detalhes bibliográficos
Autor: Dalfó, Cristina
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos: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:10459.1/65591
Acesso em linha:https://doi.org/10.1016/j.laa.2018.12.035
http://hdl.handle.net/10459.1/65591
Access Level:acceso abierto
Palavra-chave:Moore graphs
Distance-regular graph
Outindependent graph
Descrição
Resumo:This is a survey on some known properties of the possible Moore graph (or graphs) ϒ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ϒ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ϒ. Besides, ϒ is an edge-distance-regular graph.