On linear layout of bicube and construction of optimal incomplete bicube

Abstract

The generalized hypercube networks are hypercube like networks possessing superior parametrical properties over hypercube. In order to achieve the superiority, almost every generalized hypercube network compromises on the symmetricity on both nodes and edges. However, bicube, a variant of hypercube network comprises of many advantageous properties, is the main focus of our work. The aim of this work is to compute the linear layout of bicube, by utilizing its edge isoperimetric properties. As a consequence, we propose an incomplete interconnection network, the optimal incomplete bicube. We investigate the relationship of edge isoperimetric properties between bicube and optimal incomplete bicube. Further, graph theoretical properties of paramount importance is evaluated for the proposed incomplete hypercube variant.