The Fibonacci Hypercube is defined as the polytope determined by the convex hull of the “Fibonacci” strings, i.e., binary strings of length n having no consecutive ones. We obtain an efficient characterization of vertex adjacency and use this to study the graph of the Fibonacci Hypercube. In particular we discuss a decomposition of the graph into self-similar subgraphs that are also graphs of F...

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formu...

Abstract: We first study the relationship between the k-Fibonacci numbers and the elements of a subset of Q. Later, and since generally studies that are made on the Fibonacci sequences consider that these numbers are integers, in this article, we study the possibility that the index of the k-Fibonacci number is fractional; concretely, 2n+1 2 . In this way, the k-Fibonacci numbers that we obtain...

The Fibonacci cube [6] is a new class of graphs that are inspired by the famous numbers. Because of the rich properties of the Fibonacci numbers [1], the graph also shows interesting properties. For a graph with AT nodes, it is known [6] that the diameter, the edge connectivity, and the node connectivity of the Fibonacci cube are in the order of 0(log N), which are similar to the Boolean cube (...

In this paper, we suggest a lower and an upper bound for the Generalized Fibonaccip-Sequence, for different values of p. The Fibonacci-p-Sequence is a generalization of the Classical Fibonacci Sequence. We first show that the ratio of two consecutive terms in generalized Fibonacci sequence converges to a p-degree polynomial and then use this result to prove the bounds for generalized Fibonacci-...

Two diierent factorizations of the Fibonacci innnite word were given independently in 10] and 6]. In a certain sense, these factorizations reveal a self-similarity property of the Fibonacci word. We rst describe the intimate links between these two factorizations. We then propose a generalization to characteristic sturmian words. R esum e. Deux factorisations du mot de Fibonacci ont et e donn e...

In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For hh = 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet’s formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained. 2000 Mathematical Subje...

We show that if w is a factor of the infinite Fibonacci word, then the least period of w is a Fibonacci number.

In this study, new properties of Fibonacci numbers is given. Also, generalization of some properties of Fibonacci numbers is investigated with binomial coefficiations. Mathematics Subject Classification: 11B39, 11B65