The Fibonacci dimension fdim(G) of a graph G is introduced as the smallest integer f such that G admits an isometric embedding into Γf , the f -dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of the isometric and lattice dimension, provide a combinatorial characterization of the Fibonacci dimension using properties of an associated graph, and establish ...

In a recent paper, Kalman [3] derives many interesting properties of generalized Fibonacci numbers. In this paper, we take a different approach and derive some other interesting properties of matrices of generalized Fibonacci numbers. As an application of such properties, we construct an efficient algorithm for computing matrices of generalized Fibonacci numbers. The topic of generalized Fibona...

For a complexity function C, the lower and upper C-complexity rates of an infinite word x are C?(x)=lim infn??C(x?n)n,C¯(x)=lim supn??C(x?n)nrespectively. Here x?n is prefix length n. We consider case C=AN, nondeterministic automatic complexity. If these strictly between 0 1?2, we call them intermediate. Our main result that words having intermediate AN-rates exist, viz. Fibonacci Tribonacci wo...

In this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers. c © 2007 Elsevier Ltd. All rights reserved.

In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.

A Wavelet tree allows direct access to the underlying file, resulting in the fact that the compressed file is not needed any more. We adapt, in this paper, the Wavelet tree to Fibonacci Codes, so that in addition to supporting direct access to the Fibonacci encoded file, we also increase the compression savings when compared to the original Fibonacci compressed file.

We give an explicit formula for the figure of merit ρN of 2-dimensional rank 2 lattice rules in terms of continued fractions for rational numbers. Further we generalize Fibonacci lattice rules to rank 2 Fibonacci lattice rules which have the same ratio of the figure of merit to the number of points as the classical Fibonacci lattice rule.

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported ...

For a binary word f , let Qd(f) be the subgraph of the d-dimensional cube Qd induced on the set of all words that do not contain f as a factor. Let Gn be the set of words f of length n that are good in the sense that Qd(f) is isometric in Qd for all d. It is proved that limn→∞ |Gn|/2 exists. Estimates show that the limit is close to 0.08, that is, about eight percent of all words are good.

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.