The crossing number of locally twisted cubes

TL;DR

This paper investigates the crossing number of locally twisted cubes, providing new upper and lower bounds, thereby advancing understanding of graph drawings related to hypercube variants.

Contribution

It introduces bounds for the crossing number of locally twisted cubes, a variant of hypercube, extending previous work on hypercube crossing numbers.

Findings

Established new upper bounds for the crossing number.

Derived lower bounds for the crossing number.

Enhanced understanding of graph drawing complexity for hypercube variants.

Abstract

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.