Changing and unchanging the diameter of a hypercube

In a network of processors representing a massively parallel computer, the speed of communication is related to the diameter of the underlying graph. The authors investigate how the diameter of the hypercube Qn is affected by the removal of edges (presence of edge faults). In particular, they calculate the least number of edges whose removal increases the diameter and show that asymptotically most of the edges of Qn may be removed without changing the diameter. For this purpose, a new family of spanning subgraphs of Qn of minimum diameter are constructed from pairs of broadcast trees. The corresponding invariants for edge addition to hypercubes are also determined.