The crossing number of \(P(N,3)\)
The authors show that the crossing number of the generalized Petersen graph \(P(3k+ h,3)\) is \(k+h\) if \(h= 0\) or \(2\), \(k+3\) if \(h=1\), for each \(k> 2\), except that \(P(9,3)\) has crossing number \(2\). They comment as follows: A few years ago \textit{S. Fiorini} [Ann. Discrete Math. 30, 225-241 (1986; Zbl 0595.05030)] claimed to have determined the crossing numbers of certain families of generalized Petersen graphs. Unfortunately, his paper contains one serious mistake that invalidates the principal results. Our aim in this article is to present correct proofs of the main statements in Fiorini's paper, and to extend these results by determining the crossing numbers of a family of graphs for which Fiorini had only claimed upper and lower bounds.
scientific article; zbMATH DE number 1773386