The Diameter of Cyclic Kautz Digraphs
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diam...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| 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:10459.1/463245 |
| Acceso en línea: | https://doi.org/10.1016/j.endm.2015.06.044 https://hdl.handle.net/10459.1/463245 |
| Access Level: | acceso abierto |
| Palabra clave: | Kautz digraph Diameter Line digraphs Partial line digraphs |
| Sumario: | A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs M CK(d, l) and it is derived from the Kautz digraphs K(d, l). It is well-known that the Kautz digraphs K(d, l) have the smallest diameter among all digraphs with their number of vertices and degree. Here we define the cyclic Kautz digraphs CK(d, l), whose vertices are labeled by all possible sequences a1 . . . al of length l, such that each character ai is chosen from an alphabet con taining d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 l = al. |
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