The Twisted N-Cube with Application to Multiprocessing

We show that by exchanging any two independent edges in any shortest cycle of the n-cube (n 2 3), its diameter decreases by one unit. This leads us to define a new class of n-regular graphs, denoted Ten, with Zn vertices and diameter n 1, which has the (n l)-cube as subgraph. Other properties of TQ,, such as connectivity and the lengths of the disjoints paths are also investigated. Moreover, we show that the complete binary tree on 2" 1 vertices, which is not a subgraph of the n-cube, is a subgraph of TQ,,. Finally, we discuss how these results can be used to enhance existing hypercube multiprocessors.