On d-Fibonacci digraphs

C. Dalfó (Departament de Matemàtica, Universitat de Lleida, Igualada (Barcelona), Catalonia)
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)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications

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.