Genus of The Hypercube Graph And Real Moment-Angle Complexes

TL;DR

This paper calculates the genus of hypercube graphs using real moment-angle complexes and provides bounds for related quotient graphs, advancing topological graph theory and combinatorics.

Contribution

It introduces a novel method to compute the genus of hypercube graphs via real moment-angle complexes and establishes bounds for quotient graph genera.

Findings

Calculated the genus of hypercube graphs $Q_n$.

Provided an upper bound for the genus of quotient graphs $Q_n/C_n$.

Abstract

In this paper we demonstrate a calculation to find the genus of the hypercube graph $Q_n$ using real moment-angle complex $\mathcal{Z}_\mathcal{K}(D^1,S^0)$ where $\mathcal{K}$ is the boundary of an $n$-gon. We also calculate an upper bound for the genus of the quotient graph $Q_n/C_n$, where $C_n$ represents the cyclic group with $n$ elements.