An upper bound for the crossing number of bubble-sort graph Bn

TL;DR

This paper establishes an upper bound for the crossing number of the n-dimensional bubble-sort graph Bn, contributing to the understanding of its geometric complexity and drawing properties.

Contribution

It provides a new upper bound for the crossing number of Bn, extending previous work on hypercube graphs to bubble-sort graphs.

Findings

Derived an explicit upper bound for Bn's crossing number

Improves understanding of Bn's geometric complexity

Builds on methods used for hypercube graphs

Abstract

The 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 59, 145-161 (2008)], we give an upper bound of the crossing number of n-dimensional bubble-sort graph Bn.