The crossing number of pancake graph $P_4$ is six

TL;DR

This paper determines the exact crossing number of the pancake graph P4, which is six, providing precise topological information relevant for parallel computer interconnections.

Contribution

It establishes the exact crossing number of the pancake graph P4 for the first time, filling a gap in graph topology knowledge.

Findings

The crossing number of P4 is exactly six.

Provides a method for calculating crossing numbers of similar graphs.

Enhances understanding of pancake graph topology for computer interconnection networks.

Abstract

The {\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six.