Discussiones Mathematicae Graph Theory 31(2) (2011) 239-252
doi: 10.7151/dmgt.1542

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ON THE CROSSING NUMBERS OF G[¯] Cn FOR GRAPHS G ON SIX VERTICES

Emília Drazenská and  Marián Klešč

Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University, 042 00 Košice, Slovak Republic
e-mail: Emilia.Drazenska@tuke.sk
Marian.Klesc@tuke.sk

Abstract

The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The crossing numbers of G[¯] Cn for some graphs G on five and six vertices and the cycle Cn are also given. In this paper, we extend these results by determining crossing numbers of Cartesian products G[¯] Cn for some connected graphs G of order six with six and seven edges. In addition, we collect known results concerning crossing numbers of G [¯] Cn for graphs G on six vertices.

Keywords: graph, cycle, drawing, crossing number, Cartesian product.

2010 Mathematics Subject Classification: 05C10.

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Received 30 November 2009
Revised 29 April 2010
Accepted 30 April 2010