On $d$-Fibonacci digraphs
Combinatorics
2019-09-17 v1 Number Theory
Abstract
The -Fibonacci digraphs , introduced here, have the number of vertices following 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, has diameter and is semi-pancyclic, that is, it has a cycle of every length between 1 and , with . Moreover, it turns out that several other numbers of (of closed -walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the -Fibonacci digraphs.
Cite
@article{arxiv.1909.06766,
title = {On $d$-Fibonacci digraphs},
author = {C. Dalfó and M. A. Fiol},
journal= {arXiv preprint arXiv:1909.06766},
year = {2019}
}