On the panconnected properties of the Augmented cubes

Abstract

Abstract—Many topologies have been proposed to balance the performance and some cost parameters. Hypercubes are widely studied in interconnection networks [8], [9]. Augmented cubes are derivatives of hypercubes with good geometric nature and retain all the favorable properties of the hypercube. In this paper, we consider the path embedding problem with fixed endpoints in the Augmented cube AQn. For any two distinct vertices x, y in AQn, let dAQn(x, y) be the length of the shortest path between x and y. We show that there exists a path of length l joining x and y for every l satisfying dAQn(x, y) l |V (AQn)| − 1. As a consequence of it, AQn is edge pancyclic.