Efficient hypercube algorithms are developed for the following image transformations: shrinking, expanding, translation, rotation, and scaling. A 2k−step shrinking and expanding of a gray scale N×N image can be done in O (k) time on an N2 processor MIMD hypercube and in O (logN) time on an SIMD hypercube. Translation, rotation, and scaling of an N×N image take O (logN) time on an N2 processor h...

The boolean hypercube is a particularly versatile network for parallel computing. It is well known that multidimensional grid machines can be simulated on a hypercube with no communications overhead. In this paper it is shown that every bounded-degree tree can be simulated on the hypercube with constant communications overhead. In fact, the proof shows that every bounded-degree graph with an O(...

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties these polynomials—among others, a graph interpretation matrix generators. Moreover, present connections with Pascal’s triangle.

Many theoretical-based comparison studies, relying on graph structural and algorithmic properties, have been conducted for the hypercube and the star graph. None of these studies, however, have considered real working conditions and implementation limits. We have compared the performance of the star and hypercube networks for different message lengths and number of virtual channels, and conside...

This paper introduces a new concept called routing functions, which have a close relation to one-to-many disjoint paths in networks. By using a minimal routing function, a maximal number of disjoint paths whose maximal length is minimized in the worst case can be constructed in the hypercube and the folded hypercube. The end nodes of the paths constructed for the hypercube are not necessarily d...

Hypergeometric functions are an important tool in many branches of pure and applied mathematics, and they encompass most special functions, including the Chebyshev polynomials. There are also well-known connections between Chebyshev polynomials and sequences of numbers and polynomials related to Fibonacci numbers. However, to my knowledge and with one small exception, direct connections between...