五阶图与星图的笛卡尔积交叉数

The Crossing Numbers of Cartesian Products of Stars with a 5-Vertex Graph

中文关键词:  图  画法  交叉数  笛卡尔积  星图.

英文关键词:graph  drawing  crossing number  Cartesian products  star.

中文摘要:

      本文首先计算图$H_{n}$的交叉数,再通过收缩的方法,得到了$cr(G_{13}\times S_{n})=4\lfloor\frac{n}{2}\rfloor\lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n}{2}\rfloor$,这个结果填补了由~Mari\'{a}n Kle\v{s}\v{c} 给出的五阶图与星图的笛卡尔积交叉数列表中的一个空白.

英文摘要:

      In this paper, we compute the crossing number of a specific graph $H_{n}$, and then by contraction, we obtain the conclusion that ${\rm cr}(G_{13}\times S_{n})=4\lfloor\frac{n}{2}\rfloor\lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n}{2}\rfloor$. The result fills up the blank of the crossing numbers of Cartesian products of stars with all 5-vertex graphs presented by Mari\'{a}n Kle\v{s}\v{c}.