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...
| Autores: | , , , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2024 |
| 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:2117/426346 |
| Acesso em linha: | https://hdl.handle.net/2117/426346 https://dx.doi.org/10.1016/j.dam.2024.06.001 |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
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