On the permutation cycle structures for almost Moore digraphs of degrees 4 and 5
Almost Moore digraphs of degree d and diameter k, for short (d, k)-digraphs, appear in the degree/diameter problem as a class of extremal directed graphs. Their order is one less than the unattainable Moore bound M(d, k) = 1 + d + · · · + d k . So far, their existence has only been shown for k = 2....
| Autores: | ; ; |
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| Tipo de documento: | Artículo |
| Estado: | Published version |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | 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:10459.1/465425 |
| Acceso en línea: | https://doi.org/10.47443/dml.2023.142 https://hdl.handle.net/10459.1/465425 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Digraphs Moore bound Degree/diameter problem |
| Sumario: | Almost Moore digraphs of degree d and diameter k, for short (d, k)-digraphs, appear in the degree/diameter problem as a class of extremal directed graphs. Their order is one less than the unattainable Moore bound M(d, k) = 1 + d + · · · + d k . So far, their existence has only been shown for k = 2. Their nonexistence has been proven for k = 3, 4 and for d = 2, 3, when k ≥ 3. In this paper, we study the possible cycle structures of the permutation of repeats for the (4, k) and (5, k)-digraphs. |
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