Geodesic
The crossing numbers of products of a 5-vertex graph with paths and cycles
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 59-69

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There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with "small" graphs. Let H be the 5-vertex graph defined from K₅ by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H × Pₙ and H × Cₙ, showing that in the general case the corresponding crossing numbers are 3n-1, and 3n for even n or 3n+1 if n is odd.
Keywords: graph, drawing, crossing number, path, cycle, Cartesian product 
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Klešč, Marián. The crossing numbers of products of a 5-vertex graph with paths and cycles. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 59-69. http://geodesic.mathdoc.fr/item/DMGT_1999_19_1_a4/