Transitivity of Varietal Hypercube Networks

TL;DR

This paper proves that the varietal hypercube network $VQ_n$ is vertex-transitive, demonstrating its high symmetry and potential advantages over other hypercube variants for interconnection network design.

Contribution

The paper establishes the vertex-transitivity of $VQ_n$, a variant of the hypercube, highlighting its symmetrical properties and superiority for network applications.

Findings

$VQ_n$ is vertex-transitive.

$VQ_n$ has better properties than $Q_n$ with the same size.

$VQ_n$ is superior to crossed cube in symmetry.

Abstract

The varietal hypercube $VQ_n$ is a variant of the hypercube $Q_n$ and has better properties than $Q_n$ with the same number of edges and vertices. This paper proves that $VQ_n$ is vertex-transitive. This property shows that when $VQ_n$ is used to model an interconnection network, it is high symmetrical and obviously superior to other variants of the hypercube such as the crossed cube.