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关于六阶图与星的笛卡儿积交叉数 被引量：2

On the crossing number of products of a graph of order 6 and the star
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摘要 通过在完全图K4的某一条边上增加2个顶点得到一个六阶图F.分别连结F六个顶点与其他n个顶点得到一类特殊的图Hn.证明Hn的交叉数为Z(6,n)+n并由此确定且证明F×Sn的交叉数为Z(6,n)+2n. The crossing number of Cartesian products of the graph order 6 and star, presently, was proved only for that of several graphs order 6 which are few edges and star. We add two vertices to an edge of K4 to obtain a graph F which is order 6. By connecting the 6 vertices of graph F to other n vertices will obtain a special family of graph denoted by Hn. In this paper, we proved that the crossing number of Hn is Z（6, n）＋n and thereout we attested the crossing number of F×Sn is Z（6, n）＋2n.
作者 张莉茜 李波 黄元秋
机构地区 湖南师范大学数学与计算机科学学院
出处 《湖南文理学院学报（自然科学版）》 CAS 2008年第1期16-19,共4页 Journal of Hunan University of Arts and Science(Science and Technology)
基金 国家自然科学基金资助项目(10771062) 教育部"新世纪优秀人才支持计划"项目
关键词 图 画法 交叉数 星 笛卡儿积 Graph Drawing Crossing number Star Cartesian products
分类号 O157.5 [理学—基础数学]
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参考文献3

二级参考文献22

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共引文献8

同被引文献11

  • 1周智勇,肖文兵,黄元秋.星图S_5及5个六阶图与路的笛卡儿积图的交叉数[J].湖南文理学院学报（自然科学版）,2007,19(1):1-4. 被引量：5
  • 2J.A. Bondy, U.S.R. Murty. Graph theory with application. New York: Macmillan London and Elsevier, 1979.
  • 3Garey M R, Johnson D S. Crossing number is NP-complete. SIAM J. Alg. Disc.Meth., 1983, 4(3):312-316.
  • 4Kleitman D J. The crosing number of K5,n. J.Graph Series B, 1970, 9:315-323.
  • 5Huang Y Q, Zhao T L. The crossing number of K1,4,n. Disc.Math, 2008, 308(9):1634-1638.
  • 6BOKAL D. On the crossing numbers of Cartesian products with trees. J Graph Theory, 2007, 56:287-300.
  • 7M. Klesc. The join of graphs and crossing nembers. Discrete Mathematics, 2007, (23), 349-355.
  • 8M. Klesc. The crossing numbers of products of path and stars with 4-vertex graphs [J]. J.Graph Theory. 18(6)(1994), 605-614.
  • 9M. Klesc. The crossing numbers of Cartesian products of paths with 5-vertex graphs [J].Discrete Mathematics. 233(2001), 353-359.
  • 10吕胜祥,黄元秋.K_(2,4)×S_n的交叉数[J].系统科学与数学,2010,30(7):929-935. 被引量：11

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湖南文理学院学报（自然科学版）
2008年 第1期

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