On large regular (1,1,k)-mixed graphs

An (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and out-degree z, and diameter k. In this paper, we study the case r = z = 1, proposing some new constructions of (1, 1, k)-mixed graphs with a large number of vertices N. Our study is based on computer techniques for...

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Detalles Bibliográficos
Autores: Dalfó Simó, Cristina|||0000-0002-8438-9353, Erskine, Grahame, Exoo, Geoffrey, Fiol Mora, Miquel Àngel|||0000-0003-1337-4952, López Lorenzo, Nacho, Messegué Buisan, Arnau|||0000-0002-7425-7592, Tuite, James
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/426346
Acceso en línea:https://hdl.handle.net/2117/426346
https://dx.doi.org/10.1016/j.dam.2024.06.001
Access Level:acceso abierto
Palabra clave:Graph theory
Mixed graph
Moore bound
Cayley graph
Lift graph
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Descripción
Sumario:An (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and out-degree z, and diameter k. In this paper, we study the case r = z = 1, proposing some new constructions of (1, 1, k)-mixed graphs with a large number of vertices N. Our study is based on computer techniques for small values of k and the use of graphs on alphabets for general k. In the former case, the constructions are either Cayley or lift graphs. In the latter case, some infinite families of (1, 1, k)-mixed graphs are proposed with diameter of the order of 2 log2 N.