Routing properties of supercubes

Abstract Usually each vertex of the ( s +1)-dimensional hypercube is labeled with a unique integer k with 0⩽ k ⩽2 s +1 −1. The supercube S N of N nodes with 2 s N ⩽2 s +1 is constructed by merging nodes u and u −2 s , with N ⩽ u ⩽2 s +1 −1, in the ( s +1)-dimensional hypercube into a single node labeled as u −2 s and leaving other nodes in the ( s +1)-dimensional hypercube unchanged. In this paper, we give the exact distance between any two nodes of supercube and present a new shortest path routing algorithm on S N . Then we show how to construct κ ( S N ) disjoint paths between any two nodes of the supercube, where κ ( S N ) is the connectivity of S N . Finally, we compute the wide diameter and the fault diameter of S N . We show that both the wide diameter and the fault diameter are equal to s +2 if N ∈{2 s +1 −2 i +1∣0⩽ i ⩽ s −1} and s +1 otherwise.