The crossing number of folded hypercubes

TL;DR

This paper investigates the crossing number of the n-dimensional folded hypercube graph, providing bounds that help understand its complexity and drawing properties in graph theory.

Contribution

It establishes new upper and lower bounds for the crossing number of the folded hypercube, advancing knowledge on its geometric and combinatorial structure.

Findings

Derived bounds for the crossing number of $FQ_n$

Enhanced understanding of folded hypercube complexity

Contributes to graph drawing theory

Abstract

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. The {\it $n$-dimensional folded hypercube} $FQ_n$ is a graph obtained from $n$-dimensional hypercube by adding all complementary edges. In this paper, we obtain upper and lower bounds of the crossing number of $FQ_n$.