Nonexistence of almost Moore digraphs of degrees 4 and 5 with self-repeats
An almost Moore (d,k)-digraph is a regular digraph of degree d>1, diameter k>1 and order N(d,k)=d+d2+⋯+dk. So far, their existence has only been shown for k=2, whilst it is known that there are no such digraphs for k=3, 4 and for d=2, 3 when k≥3. Furthermore, under certain assumptions, the non...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| 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:2117/386781 |
| Acceso en línea: | https://hdl.handle.net/2117/386781 https://dx.doi.org/10.37236/11335 |
| Access Level: | acceso abierto |
| Palabra clave: | Directed graphs Grafs dirigits Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | An almost Moore (d,k)-digraph is a regular digraph of degree d>1, diameter k>1 and order N(d,k)=d+d2+⋯+dk. So far, their existence has only been shown for k=2, whilst it is known that there are no such digraphs for k=3, 4 and for d=2, 3 when k≥3. Furthermore, under certain assumptions, the nonexistence for the remaining cases has also been shown. In this paper, we prove that (4,k) and (5,k)-almost Moore digraphs with self-repeats do not exist for k≥5. |
|---|