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

The binary hypercube Q(n) has a small diameter, but a relatively large numb er of links. Because of this, efforts have been made to determine the maxim um number of links that can be deleted without increasing the diameter. How ever, the resulting networks are not vertex-symmetric. We propose a family of vertex-symmetric spanning subnetworks of Q(n), whose diameter differs fr om that of Q(n) by only a small constant factor. When n = 2(k), the cube-co nnected cycles network of dimension n is a vertex-symmetric spanning subnet work of Q(n+lg n). By selectively adding hypercube links, we obtain a degre e 6 vertex-symmetric network with diameter 3n/2. We also introduce a vertex -symmetric spanning subnetwork of Q(n-1) with degree log(2) n, diameter 3n/ 2 - 2, log(2) n-connectivity and maximal fault tolerance. This network host s Q(n-1) with dilation 2(log(2) n) - 1.