Moore mixed graphs from Cayley graphs
A Moore (r; z; k)-mixed graph G has every vertex with undirected degree r, directed in and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r; z; k) for mixed graphs. When the order of G is close to M(r; z; k) vertices, we refer to it as an almost...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| 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:10459.1/463278 |
| Acesso em linha: | https://doi.org/10.5614/ejgta.2023.11.1.15 https://hdl.handle.net/10459.1/463278 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cayley graph Line digraph Mixed graph Moore bound Spectrum |
| Resumo: | A Moore (r; z; k)-mixed graph G has every vertex with undirected degree r, directed in and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r; z; k) for mixed graphs. When the order of G is close to M(r; z; k) vertices, we refer to it as an almost Moore graph. The first part of this paper is a survey about known Moore (and almost Moore) general mixed graphs that turn out to be Cayley graphs. Then, in the second part of the paper, we give new results on the bipartite case. First, we show that Moore bipartite mixed graphs with diameter three are distance-regular, and their spectra are fully characterized. In particular, an infinity family of Moore bipartite (1; z; 3)-mixed graphs is presented, which are Cayley graphs of semidirect products of groups. Our study is based on the line digraph technique, and on some results about when the line digraph of a Cayley digraph is again a Cayley digraph. |
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