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六阶图C_6+3K_2与P_n, C_n的联图交叉数

苏振华1,*   

  1. 1. 怀化学院数学系, 湖南怀化  418008
  • 收稿日期:2016-12-26 出版日期:2017-09-15 发布日期:2017-09-15
  • 通讯作者: 苏振华 szh820@163.com
  • 基金资助:

    湖南省自然科学基金(No. 2017JJ3251), 湖南省教育厅科研项目(No. 15C1090)

The crossing number of the join product of C_6+3K_2 with P_n and C_n

SU Zhenhua1,*   

  1. 1. Department of Mathematics, Huaihua University, Huaihua  418008, Hunan, China
  • Received:2016-12-26 Online:2017-09-15 Published:2017-09-15

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摘要：

用P_n表示n个点的路, C_n表示长为n的圈, C_6+3K_2表示 圈C_6添加三条相邻的边3K_2=C_3得到的图. 在Kleitman给出的完全二部图的交叉数cr(K_{6,n})=Z(6,n)的基础上, 得到了特殊六阶图C_6+3K_2与路P_{n}, 圈C_{n}的联图交叉数分别为 Z(6,n)+3\lfloor \frac{n}{2} \rfloor+2 与 Z(6,n)+3\lfloor \frac{n}{2} \rfloor+4.

关键词: 交叉数, 联图, 路图, 圈图

Abstract:

Let P_n be the path on n vertices, C_n be the cycle with n edges, C_6+3K_2 be the graph which is obtained from the cycle C_6 by adding three adjacent edges. In the paper, for special graph C_6+3K_2, we give the crossing numbers of its join product with the path P_n as well as the cycle C_n are Z(6,n)+3\lfloor \frac{n}{2} \rfloor+2 and Z(6,n)+3\lfloor \frac{n}{2} \rfloor+4. Our proof depends on Kleitman's results for the complete bipartite graph cr(K_{6,n})=Z(6,n).

Key words: crossing number, join product, path, cycle