### On d-Fibonacci digraphs

#### 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 ∈ {2*k* − 2, 2*k* − 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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PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.2.22

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