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.

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...