Removing edges from hypercubes to obtain vertex-symmetric networks with small diameter

The binary hypercube Qn has small diameter, but a relatively large number of links. Because of this, efforts have been made to determine the maximum number of links that can be deleted without increasing the diameter. However, the resulting networks are not vertex-symmetric. We propose a family of vertex-symmetric spanning subnetworks of Qn, whose diameter differs from that of Qn by only a small constant factor. When n=2, the cube-connected cycles network of dimension n is a vertexsymmetric spanning subnetwork of Qn+k. By selectively adding hypercube links, we obtain a degree 6 vertex-symmetric network with diameter 3 2 n . We also introduce a vertex-symmetric spanning subnetwork of Qn-1 with degree log2 n, diameter 3 2 n -2, log2 nconnectivity and maximal fault tolerance. This network hosts Qn-1 with dilation 2(log2 n)-1.