Geodesic
The Crossing Numbers of Products of Path with Graphs of Order Six
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 571-582

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The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path P_n of length n, the crossing numbers of Cartesian products G □ P_n for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G □ P_n for graphs G of order six are studied. Let H denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product H □ P_n is 2(n − 1). In addition, the crossing numbers of G □ P_n for fourty graphs G on six vertices are collected.
Keywords: graph, drawing, crossing number, Cartesian product, path, tree 
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Klešč, Marián; Petrillová, Jana. The Crossing Numbers of Products of Path with Graphs of Order Six. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 571-582. http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a6/