The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the expressions of Fibonacci graphs and eventually find their shortest representations. With that end in view, we describe the number of methods for generating Fibonacc...

The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the expressions of Fibonacci graphs and eventually find their shortest representations. With that end in view, we describe the optimal decomposition method for generati...

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, Fp(n), and their sums, Pn i1⁄41F pðiÞ, and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sum...

Although it has been studied extensively, Pascal's triangle remains fascinating to explore and there always seems to be some new aspects that are revealed by looking at it closely. In this paper we shall examine a few nice properties of the so-called Fibonacci diagonals, that is, those slant lines whose entries sum to consecutive terms of the Fibonacci sequence. We adopt throughout our text the...

In this paper we investigate the inherent complexity of the priority queue abstract data type. We show that, under reasonable assumptions, there exist sequences of n Insert, n Delete, m DecreaseKey and t FindMin operations, where 1 ≤ t ≤ n, which have Ω(nlogt + n + m) complexity. Although Fibonacci heaps do not achieve this bound, we present a modified Fibonacci heap which does, and so is optim...

The generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all vertices that contain a given binary word f as a factor; the generalized Lucas cube Qd( ↽Ð f ) is obtained from Qd by removing all the vertices that have a circulation containing f as a factor. In this paper the Wiener index of Qd(1) and the Wiener index of Qd( ↽Ð 1) are expressed as functions of the o...

What is the ANZL Algorithm? It is a genuine result of our work which is theoretically and practically proved. By using the ANZL Algorithm, we can test whether a given number belongs to Lucas’s series. It can also be used to find a sequence of Lucas’s numbers, starting from any number . If a given number completes the relation , we can say that it is a Lucas number and we mark it as . From the p...

Coupled Fibonacci sequences of lower order have been generalized in number of ways.In this paper the Multiplicative Coupled Fibonacci Sequence has been generalized for r t h order with some new interesting properties. MSC: 11B39 • 11B37 • 11B99

In this article, the Apostol Bernoulli-Fibonacci polynomials are defined and various properties of obtained. Furthermore, Euler-Fibonacci numbers found. addition, harmonic-based F exponential generating functions for numbers.

Abstract: Let be a Gaussian Fibonacci skew-circulant matrix, and be a Gaussian Fibonacci left skew-circulant matrix, and both of the first rows are , where is the th Gaussian Fibonacci number, and is a nonnegative integer. In this paper, by constructing the transformation matrices, the explicit determinants of and are expressed. Moreover, we discuss the singularities of these matrices and the i...