A survey on the missing Moore graph

This is a survey on some known properties of the possible Moore graph (or graphs) ¿ 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 ¿ induced by a vertex subset C, the following graphs are distance-regular:...

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Detalhes bibliográficos
Autor: Dalfó Simó, Cristina|||0000-0002-8438-9353
Formato: artículo
Fecha de publicación:2019
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:2117/127212
Acesso em linha:https://hdl.handle.net/2117/127212
https://dx.doi.org/10.1016/j.laa.2018.12.035
Access Level:acceso abierto
Palavra-chave:Graph theory
Matrices
Moore graphs
Distance-regular graph
Outindependent graph
Spectral graph theory
Automorphisms
Grafs, Teoria de
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Descrição
Resumo:This is a survey on some known properties of the possible Moore graph (or graphs) ¿ 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 ¿ 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 ¿. Besides, ¿ is an edge-distance-regular graph.