On the Crossing Numbers of Cartesian Products of Small Graphs with Paths, Cycles and Stars

TL;DR

This paper advances the understanding of crossing numbers by determining the crossing numbers for fifteen families of Cartesian product graphs involving small graphs and paths, cycles, and stars.

Contribution

It provides new crossing number results for fifteen families of Cartesian product graphs with small graphs having five or more vertices.

Findings

Crossing numbers for fifteen new graph families are established.

Results fill gaps in the existing literature for graphs with five or more vertices.

Enhances understanding of graph crossing numbers in Cartesian products.

Abstract

There has been significant research dedicated towards computing the crossing numbers of families of graphs resulting from the Cartesian products of small graphs with arbitrarily large paths, cycles and stars. For graphs with four or fewer vertices, these have all been computed, but there are still various gaps for graphs with five or more vertices. We contribute to this field by determining the crossing numbers for fifteen such families.