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星图 S 4的交叉数
引用本文:吕波,徐喜荣,杨元生,张科,郑百功.星图 S 4的交叉数[J].大连理工大学学报,2014,54(4):469-476.
作者姓名:吕波  徐喜荣  杨元生  张科  郑百功
作者单位:大连理工大学电子信息与电气工程学部计算机科学与技术学院
基金项目:国家自然科学基金资助项目(61170303,60973014,10671191).
摘    要:研究网络拓扑结构图星图S4的交叉数问题.首先构造星图S4好的画法,得到了S4交叉数的上界,然后给出了S4交叉数下界的数学证明,最终得到S4的交叉数的精确值为8.同时给出了与其具有同构关系的图S4,3和图A4,3的交叉数.

关 键 词:交叉数  画法  Star图  (n  k)-Star图  Arrangement图

Crossing number of Star graph S 4
L Bo,XU Xirong,YANG Yuansheng,ZHANG Ke,ZHENG Baigong.Crossing number of Star graph S 4[J].Journal of Dalian University of Technology,2014,54(4):469-476.
Authors:L Bo  XU Xirong  YANG Yuansheng  ZHANG Ke  ZHENG Baigong
Institution:L Bo;XU Xi-rong;YANG Yuan-sheng;ZHANG Ke;ZHENG Bai-gong;School of Computer Science and Technology,Faculty of Electronic Information and Electrical Engineering,Dalian University of Technology;
Abstract:The problem of the crossing number about network topological structure graph S 4 is studied. Firstly, by constructing a good drawing of Star graph S 4, an upper bound of the crossing number of S 4 is obtained. Then, the lower bound of the crossing number of S 4 is obtained by mathematical proof. Lastly, the conclusion is drawn that the exact value of the crossing number of S 4 is 8. Meanwhile, the crossing numbers of graph S 4,3 and graph A 4,3 , which are isomorphic to S 4, are given.
Keywords:crossing number  drawing  Star graph  ( n  k )-Star graph  Arrangement graph
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