| 一个特殊6点图Q与nK_1,P_n及C_n的联图交叉数 |
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| 引用本文： | 周志东,李龙. 一个特殊6点图Q与nK_1,P_n及C_n的联图交叉数[J]. 运筹学学报, 2016, 20(4): 115-126. DOI: 10.15960/j.cnki.issn.1007-6093.2016.04.014 |
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| 作者姓名： | 周志东 李龙 |
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| 作者单位： | 1. 衡阳师范学院数学与统计学院, 湖南 衡阳 421002 |
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| 基金项目： | 国家自然科学基金青年项目(No. 11401185), 湖南省重点建设学科项目, 湖南省重点实验室“智能信息处理与应用”, 湖南省自然科学基金青年人才联合培养基金(No. 14JJ6039), 衡阳师范学院科研启动基金(No. 13B39) |
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| 摘 要： | 图的交叉数是图的一个重要参数,研究图的交叉数问题是拓扑图论中的前沿难题.确定图的交叉数是NP-难问题,因为其难度,能够确定交叉数的图类很少.通过圆盘画法途径,确定了一个特殊6点图与n个孤立点nK_1,路P_n及圈C_n的联图的交叉数分别是cr(Q+nK_1)=Z(6,n)+2[n/2],cr(Q+P_n)=Z(6,n)+2[n/2]+1及cr(Q+C_n)=Z(6,n)+2[n/2]+3.
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| 关 键 词： | 画法 交叉数 圆盘画法 联图 路 圈 |
| 收稿时间： | 2016-02-29 |
On the crossing numbers of join of the special graph on six vertices with nK_1, P_n or C_n |
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| ZHOU Zhidong,LI Long. On the crossing numbers of join of the special graph on six vertices with nK_1, P_n or C_n[J]. OR Transactions, 2016, 20(4): 115-126. DOI: 10.15960/j.cnki.issn.1007-6093.2016.04.014 |
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| Authors: | ZHOU Zhidong LI Long |
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| Affiliation: | 2. College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, Hunan, China |
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| Abstract: | The crossing numbers of a graph is a vital parameter and a hard problem in the forefront of topological graph theory. Determining the crossing number of an arbitrary graphs is NP-complete problem. Because of its difficultly, the classes of graphs whose crossing number have been determined are very scarce. In this paper, for the special graph Q on six vertices, we through the disk drawing method to prove that the crossing numbers of its join with n isolated vertices as well as with the path P_{n} and with the cycle C_{n} are cr(Q+nK_{1})=Z(6,n)+2lfloorfrac{n}{2}rfloor, cr(Q+P_{n})=Z(6,n)+2lfloorfrac{n}{2}rfloor+1 and cr(Q+C_{n})=Z(6,n)+2lfloorfrac{n}{2}rfloor+3, respectively. |
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| Keywords: | drawing crossing number disk drawing joint graph path cycle |
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