| $K_{5}\times S_{n}$ 的交叉数 |
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| 引用本文： | 吕胜祥,黄元秋.$K_{5}\times S_{n}$ 的交叉数[J].数学研究及应用,2008,28(3):445-459. |
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| 作者姓名： | 吕胜祥 黄元秋 |
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| 作者单位： | 北京交通大学数学系, 北京 100044;湖南师范大学数学与计算机科学学院, 湖南 长沙 410081 |
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| 基金项目： | 国家自然科学基金(No.10771062); 新世纪优秀人才支持计划. |
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| 摘 要： | 把完全图$K_{5}$的五个顶点与另外$n$个顶点都联边得到一类特殊的图$H_{n}$.文中证明了$H_{n}$的交叉数为$Z(5,n)+2n+\lfloor \frac{n}{2}\rfloor+1$,并在此基础上证明了$K_{5}$与星$K_{1,n}$的笛卡尔积的交叉数为$Z(5,n)+5n+\lfloor\frac{n}{2} \rfloor+1$.
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| 关 键 词： | 图 交叉数 星 笛卡尔积. |
| 收稿时间： | 2006/6/19 0:00:00 |
| 修稿时间： | 2007/3/22 0:00:00 |
On the Crossing Numbers of $K_5\times S_n$ |
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| L\"{U} Sheng Xiang and HUANG Yuan Qiu.On the Crossing Numbers of $K_5\times S_n$[J].Journal of Mathematical Research with Applications,2008,28(3):445-459. |
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| Authors: | L\"{U} Sheng Xiang and HUANG Yuan Qiu |
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| Institution: | Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China;Department of Mathematics, Normal University of Hunan, Hunan 410081, China |
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| Abstract: | By connecting the $5$ vertices of $K_{5}$ to other $n$ vertices, we obtain a special family of graph denoted by $H_{n}$. This paper proves that the crossing number of $H_{n}$ is $Z(5,n)+2n+\lfloor \frac{n}{2} \rfloor+1$, and the crossing number of Cartesian products of $K_{5}$ with star $S_{n}$ is $Z(5,n)+5n+\lfloor \frac{n}{2} \rfloor+1$. |
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| Keywords: | graph drawing crossing number star Cartesian products |
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