Hypercube structures are heavily used by parallel algorithms that require all-to-all communication. When communicating over a heterogeneous and irregular network, the performance obtained by the hypercube structure will depend on the matching of the hypercube structure to the topology of the underlying network. In this paper, we present strategies to build topology-based hypercubes structures. ...

The Hypercube Neural Network Algorithm is a novel supervised method for classification. One hypercube is defined per class in the attribute space based on the training data. Each dimension of a hypercube is set to cover the full range of values in the class. The hypercube learning is therefore a rapid, one-shot form of learning. This paper presents three versions of the algorithm: hypercube wit...

This paper analyzes a product network generated from torus and hypercube networks known as Torus embedded hypercube scalable interconnection network suitable for parallel architecture. It is shown here that how good a Torus embedded Hypercube interconnection network can be compared to the existing Mesh embedded hypercube interconnection network with minor modifications in its architecture. A co...

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...

An integer sequence (xn)n≥0 is said to be Fibonacci-like if it satisfies the binary recurrence relation xn = xn−1 + xn−2, n ≥ 2. We construct a new type of Fibonacci-like sequence of composite numbers. 1 The problem and previous results In this paper we consider Fibonacci-like sequences, that is, sequences (xn) ∞ n=0 satisfying the binary recurrence relation xn = xn−1 + xn−2, n ≥ 2. (1)

In this paper we obtain formulas for certain sums of products involving multinomial coefficients and Fibonacci numbers. The sums studied here may be regarded as generalizations of the binomial transform of the sequence comprising the even-numbered terms of the Fibonacci sequence. The general formulas, involving both Fibonacci and Lucas numbers, give rise to infinite sequences that are parameter...

For a graph G, Fibonacci Number of G is defined as the number of subsets of V (G) in which no two vertices are adjacent in G. In this paper, we first investigate the orderings of two classes of trees by their Fibonacci numbers. Using these orderings, we determine the unique tree with the second, and respectively the third smallest Fibonacci number among all trees with n vertices.

ABSTRACT Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of ...

Abstract: In this study, we present a numerical scheme to solve the telegraph equation by using Fibonacci polynomials. This method is based on the Fibonacci collocation method which transforms the equation into a matrix equation, and the unknown of this equation is a Fibonacci coefficients matrix. Some numerical examples with comparisons are included to demonstrate the validity and applicabilit...