The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, the d-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the resonance graphs of a subclass of the catacon...

As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively ...

Here, we investigate the Fibonacci numbers whose sum of aliquot divisors is also a Fibonacci number (the prime Fibonacci numbers have this property).

Fibonacci cubes, extended Fibonacci cubes, and Lucas cubes are induced subgraphs of hypercubes 9 defined in terms of Fibonacci strings. It is shown that all these graphs are median. Several enumeration results on the number of their edges and squares are obtained. Some identities involving Fibonacci 11 and Lucas numbers are also presented. © 2005 Published by Elsevier B.V. 13

Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. Indeed, Koshy gushingly refers to them as one of the “two shining stars in the vast array of integer sequences” [16, p. xi]. The second of Koshy’s “shining stars” is the Lucas numbers, a close relative of the Fibonacci numbers, about which we will say more below. The Fibonacci numbers are famous for po...

1. Robert P. Backstrom. "On the Determination of the Zeros of the Fibonacci Sequence." The Fibonacci Quarterly 4, No. 4 (1966):313-322. 2. R. D. Carmichael. "On the Numerical Factors of the Arithmetic Forms a + 3." Annals of Mathematics9 2nd Ser. 15 (1913):30-70. 3. John H. Halton. "On the Divisibility Properties of Fibonacci Numbers." The Fibonacci Quarterly 4, No. 3 (1966):217-240. 4. D.H. Le...

Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthes...