A product network defines a class of topologies that are very often used such as meshes, tori, and hypercubes, etc. This paper proposes a generalized algorithm for fault-tolerant parallel sorting in product networks. To tolerate r−1 faulty nodes, an r-dimensional product network containing faulty nodes is partitioned into a number of subgraphs such that each subgraph contains at most one fault....

A product network defines a class of topologies that are very often used such as meshes, tori, and hypercubes, etc. This paper proposes a generalized algorithm for fault-tolerant parallel sorting in product networks. To tolerate r 1 faulty nodes, an r-dimensional product network containing faulty nodes is partitioned into a number of subgraphs such that each subgraph contains at most one fault....

Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of topological spaces with horizontal, vertical, and standard product topo...

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We p...