Geodesic
The Crossing Number of The Hexagonal Graph H3,n
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 547-554

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In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings. Many authors made great efforts to investigate the crossing number (in the plane) of the Cartesian product of an m-cycle and an n-cycle, which is a special (4,4)-tiling. For other tilings, there are quite rare results concerning on their crossing numbers. This motivates us in the paper to determine the crossing number of a hexagonal graph H3,n, which is a special kind of (3,6)-tilings.
Keywords: hexagonal graph, Cartesian product, crossing number, drawing 
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Wang, Jing; Ouyang, Zhangdong; Huang, Yuanqiu. The Crossing Number of The Hexagonal Graph H3,n. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 547-554. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a16/