On d-Fibonacci digraphs
The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k -...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/357037 |
| Acesso em linha: | https://hdl.handle.net/2117/357037 https://dx.doi.org/10.5614/ejgta.2021.9.2.22 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Graph theory N-step Fibonacci number Fibonacci graph Digraph on alphabet De Bruijn digraph Line digraph Adjacency matrix Spectrum Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k - 2 and is semi-pancyclic; that is, it has a cycle of every length between 1 and l, with l ¿ {2k - 2, 2k - 1}. Moreover, it turns out that several other numbers of F(d, k) (of closed l-walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the d-Fibonacci digraphs. |
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