Abstract: Möbius cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint 2D meshes into a Möbius cube. Two major contributions of this paper are: (1) For n ≥ 1, there exists a 2 × 2 mesh that can be embedded in the n-dimensional Möbius cube with dilation 1 and expansion 1. (2) For n ≥ 4, there are two disjoint 4 × 2 meshes that can be embedded ...

In this paper, we present a strongly fault-tolerant design for the k-ary n-cube multiprocessor and examine its reconfigurability. Our design augments the k-ary n-cube with ( j ) n spare nodes; each set of j regular nodes is connected to a spare node and the spare nodes are interconnected as a ( j )-ary n-cube. Our approach utilizes the circuit-switched capabilities of the communication modules ...

In this paper we present a method for analyzing a general class of ramdom walks on the n cube and certain subgraphs of it These walks all have the property that the transition probabilities depend only on the level of the point the walk is at For these walks we derive sharp bounds on their mixing rates i e the number of steps required to guarantee that the resulting distribution is close to the...

In this paper we present a method for analyzing a general class of random Ž . walks on the n-cube and certain subgraphs of it . These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to Ž . guarantee that the resulting distrib...

In this paper we present a method for analyzing a general class of ramdom walks on the n-cube (and certain subgraphs of it). These walks all have the property that the transition probabilities depend only on the level of the point the walk is at. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to guarantee that the resulting distribution is clos...

Consider a hypergraph H d n where the vertices are points of the d-dimensional combinatorial cube n d and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of H d n , i.e., permutations of points of n d preserving the edges. In this paper we provide a complete characterization. Moreover, we consider the Colored Cube Isomorphi...