The crossing numbers of $K_m\times P_n$ and $K_m\times C_n$

TL;DR

This paper investigates the crossing numbers of the Cartesian products of complete graphs with paths and cycles, providing new insights into their minimal crossing configurations.

Contribution

It determines the crossing numbers of $K_m imes P_n$ and $K_m imes C_n$, advancing understanding of graph drawing complexities for these classes.

Findings

Derived exact crossing numbers for $K_m imes P_n$

Derived exact crossing numbers for $K_m imes C_n$

Enhanced understanding of graph crossing minimization

Abstract

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. In this paper, we study the crossing numbers of $K_{m}\times P_n$ and $K_{m}\times C_n$.