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

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.

Keywords:

• crossing number
• drawing
• generalized Petersen graph
• graph theory
• combinatorics

2010 AMS Subject Classification :

• 05C10

Acknowledgements

We are very grateful to the referees for their careful reading with corrections and useful comments. This research is supported by NSFC (60973014, 61170303).