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Zongpeng Ding and Yuanqiu Huang

Abstract

There are only few results concerning crossing numbers of join of some graphs. In this paper, for some graphs on five vertices, we give the crossing numbers of its join with n isolated vertices.

Open access

Jing Wang, Zhangdong Ouyang and Yuanqiu Huang

Abstract

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 S 1 and the Klein bottle N 2 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 H 3, n, which is a special kind of (3,6)-tilings.