The crossing number of the generalized Petersen graph P(10, 3) is six

TL;DR

This paper establishes that the crossing number of the generalized Petersen graph P(10, 3) is exactly six, providing a precise measure of its minimal edge crossings in planar drawings.

Contribution

The paper proves the exact crossing number of P(10, 3), a specific generalized Petersen graph, which was previously unknown.

Findings

Crossing number of P(10, 3) is six

Provides a method to determine crossing numbers of similar graphs

Enhances understanding of graph drawing complexity

Abstract

The crossing number of a graph is the least number of crossings of edges among all drawings of the graph in the plane. In this article, we prove that the crossing number of the generalized Petersen graph P(10, 3) is equal to 6.