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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