A class of fixed-degree Cayley-graph interconnection networks derived by pruning k-ary n-cubes

Abstract

We introduce a pruning scheme to reduce the node degree of k-ary n-cube from 2n to 4. The links corresponding to n-2 of the n dimensions are removed from each node. One of the remaining dimensions is common to all nodes and the other is selected periodically from the remaining n-1 dimensions. Despite the removal of a large number of links from the k-ary n-cube, this incomplete version still preserves many of its desirable topological properties. In this paper, we show that this incomplete k-ary n-cube belongs to the class of Cayley graphs, and hence, is node-symmetric. It is 4-connected with diameter close to that of the k-ary n-cube.