The Crossing Number of Join of the Generalized Petersen Graph P (3, 1) with Path and Cycle
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 351-370.

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There are only few results concerning the crossing numbers of join of some graphs. In this paper, the crossing numbers of join products for the generalized Petersen graph P(3, 1) with n isolated vertices as well as with the path Pn on n vertices and with the cycle Cn are determined.
Keywords: crossing number, drawing, join product, generalized Petersen graph
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Ouyang, Zhang Dong; Wang, Jing; Huang, Yuan Qiu. The Crossing Number of Join of the Generalized Petersen Graph P (3, 1) with Path and Cycle. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 351-370. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a1/

[1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan Press Ltd, London, 1976).

[2] P. Erdős and R.K. Guy, Crossing number problems, Amer. Math. Monthly 80 (1973) 52–58. doi:10.2307/2319261

[3] M.R. Garey and D.S. Johnson, Crossing number is NP-complete, SIAM J. Algebraic Discrete Methods 4 (1983) 312–316. doi:10.1137/0604033

[4] V.R. Kulli and M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87–97.

[5] D.J. Kleitman, The crossing number of K 5,n, J. Combin. Theory Ser. B 9 (1970) 315–323. doi:10.1016/S0021-9800(70)80087-4

[6] M. Klešč, The join of graphs and crossing numbers, Electron. Notes Discrete Math. 28 (2007) 349–355. doi:10.1016/j.endm.2007.01.049

[7] L. Tang, J. Wang and Y.Q. Huang, The crossing number of the join of Cm and Pn, Internat. J. Math. Com. 1 (2007) 110–116.

[8] M. Klešč and S. Schrötter, The crossing numbers of join products of paths with graphs of order four, Discuss. Math. Graph Theory 31 (2011) 321–331. doi:10.7151/dmgt.1548

[9] M. Klešč, The crossing numbers of join of the special graph on six vertice with path and cycle, Discrete Math. 310 (2010) 1475–1481. doi:10.1016/j.disc.2009.08.018

[10] M. Klešč and S. Schrötter, The crossing numbers of join of paths and cycles with two graphs of order five, Lecture Notes in Comput. Sci. 7125 (2012) 160–167. doi:10.1007/978-3-642-28212_615

[11] Y.H. Peng and Y.C. Yiew, The crossing number of P(3, 1) × Pn, Discrete Math. 306 (2006) 1941–1946. doi:10.1016/j.disc.2006.03.058