The interconnection network is an essential component of a distributed system or of a supercomputer based on large-sale parallel processing. Because in distributed systems the communication between processors is based on message exchange, the network topology is of a great importance. The interconnection network can be seen as a graph and the properties of a network can be studied using combina...

Sloane’s influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community. The sequence A001611 listing the “Fibonacci numbers + 1” contains a very large number of references and links. The sequence A000071 for the “Fibonacci numbers −1” contains an even larger number. Strangely, resentment seems to prevail between the two sequ...

Given a simple connected undirected graph G = (V , E), the Wiener index W (G) of G is defined as half the sum of the distances d(u, v) between all pairs of vertices u, v of G, where d(u, v) denotes the distance (the number of edges on a shortest path between u and v) between u, v in G. We obtain an expression for W (G), where G is a binomial tree. For Fibonacci trees and binary Fibonacci trees ...

The collision test is an important statistical test for rejecting poor random number generators. The test simulates the throwing of balls randomly into urns. A problem in applying this test is to determine the number of urns, m, and the number of balls, n, so that the test is among the most powerful possible on a computer. The problem was tackled empirically. A set of canonical congruential gen...

Ensuring that pseudorandom number generators have good randomness properties is more complicated in a multiprocessor implementationthan in the uniprocessor case. We discuss simple extensions of uniprocessor testing for SIMD parallel streams, and develop in detail a repeatability test for the SPMD paradigm. Examples of the application of these tests to an additive lagged-Fibonacci generator are ...

In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which call ordered numbers. We determine the properties numbers including relations with Leonardo, Fibonacci, and Lucas Symmetric antisymmetric Fibonacci are used in proofs. attain some well-known identities, Binet formula, generating function for these Finally, provide illustrations identities.

Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum of nonconsecutive Fibonacci numbers. This theorem induces a binary numeration system for the positive integers known as Fibonacci coding. Fibonacci code is a variable-length prefix code that is robust against insertion and deletion errors and is useful in data transmission and data compression. In this pape...

In this paper, we note that a number of unexplained and stipulative properties of the grammar (such as the Generalized Extended Projection Principle, Binary Branching, Labeling) find a functional explanation, if we view them as correlates of a general desire for the grammar to maximize trees in such a way that they result in a Fibonacci-like sequence of maximal categories. Further, we note that...

The numerical semigroup generated by relatively prime positive integers a1, . . . , an is the set S of all linear combinations of a1, . . . , an with nonnegative integral coefficients. The largest integer which is not an element of S is called the Frobenius number of S. Recently, J. M. Maŕın, J. L. Ramı́rez Alfonśın, and M. P. Revuelta determined the Frobenius number of a Fibonacci semigroup, th...