Symmetry Parameters of Various Hypercube Families

TL;DR

This paper investigates the symmetry parameters related to the distinguishing number and cost of various hypercube variants, including Hamming graphs and twisted hypercubes, to understand their symmetry properties.

Contribution

It provides new results on the symmetry parameters for multiple hypercube variants, extending the understanding of their automorphism groups.

Findings

Determined the number of 2-distinguishing colorings for various hypercube families.

Calculated the distinguishing cost for folded, enhanced, and augmented hypercubes.

Compared symmetry parameters across different hypercube variants.

Abstract

In this paper we study the symmetry parameters determining number, distinguishing number, and cost of 2-distinguishing, for some variations on hypercubes, namely Hamming graphs, powers of hypercubes, folded hypercubes, enhanced hypercubes, augmented hypercubes and locally twisted hypercubes.