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

Fici, Restivo, Silva, and Zamboni define a $k$-antipower to be word composed of $k$ pairwise distinct, concatenated words equal length. Berger Defant conjecture that for any sufficiently well-behaved aperiodic morphic $w$, there exists constant $c$ such index $i$, with block length at most $ck$ starts the $i$th position $w$. They prove their in case binary words, we extend result alphabets arbi...

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...

We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches zero, of its thickness and its Hausdorff dimension. We announce the following results and explain some key ideas that go into their proofs. The thickness tend...

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...

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula f...

The Fibonacci dimension fdim(G) of a graph G was introduced in [7] as the smallest integer d such that G admits an isometric embedding into Qd, the d-dimensional Fibonacci cube. A somewhat new combinatorial characterization of the Fibonacci dimension is given, which enables more comfortable proofs of some previously known results. In the second part of the paper the Fibonacci dimension of the r...

In the deep sub micrometer CMOS process technology, the interconnect resistance, length, and interwire capacitance are increasing significantly, which contribute to large on-chip interconnect propagation delay. Data transmitted over interconnect determine the propagation delay and the delay is very significant when adjacent wires are transitioning in opposite directions (i.e., crosstalk transit...