Diameter variability of hypercubes

A parallel and distributed system is usually represented by a graph. The maximum communication delay between any pair of processors in a parallel and distributed system can be determined by the diameter of its underlying graph. The diameter of a graph can be affected by the addition or deletion of edges. In this paper, we show that the diameter of an n-dimensional hypercube can be decreased by k with the addition of 22k−1 edges for 1≤k≤⌊n/2⌋.