On the Orchard crossing number of prisms, ladders and other related graphs

TL;DR

This paper investigates the Orchard crossing number for various cycle-based graphs, including prisms and ladders, providing insights into their crossing properties and extending understanding of graph drawing complexities.

Contribution

It introduces new results on the Orchard crossing number for prism and ladder graphs, expanding the knowledge of crossing numbers in cycle-based graph families.

Findings

Determined the Orchard crossing number for prism graphs.

Established bounds for the Orchard crossing number of ladder graphs.

Extended crossing number analysis to graphs with shared vertices and edges.

Abstract

This paper deals with the Orchard crossing number of some families of graphs which are based on cycles. These include disjoint cycles, cycles which share a vertex and cycles which share an edge. Specifically, we focus on the prism and ladder graphs.