The crossing numbers of $K_{n,n}-nK_2$, $K_{n}\times P_2$, $K_{n}\times P_3$ and $K_n\times C_4$

TL;DR

This paper determines the crossing numbers for specific complex graphs involving complete bipartite and product graphs, providing exact values or bounds for these graph classes.

Contribution

It introduces new results on the crossing numbers of certain bipartite and product graphs, expanding the understanding of graph drawing complexity.

Findings

Crossing number of $K_{n,n}-nK_2$ determined

Crossing number of $K_n\times P_2$ established

Crossing number of $K_n\times P_3$ and $K_n\times C_4$ calculated

Abstract

The crossing number of a graph $G$ is the minimum number of pairwise intersections of edges among all drawings of $G$. In this paper, we study the crossing number of $K_{n,n}-nK_2$, $K_n\times P_2$, $K_n\times P_3$ and $K_n\times C_4$.