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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
M.A. Fiol
Departament de Matematiques, Universitat Polit‘ecnica de Catalunya Barcelona Graduate School of Mathematics Institut de Matematiques de la UPC-BarcelonaTech (IMTech) Barcelona, Catalonia
Electrical & Electronics Engineering

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On d-Fibonacci digraphs C. Dalfó; M.A. Fiol
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.22

Abstract

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.
Co-Authors C. Dalfó