两类特殊联图的交叉数
发布时间：2018-08-02 16:27
【摘要】：图的交叉数问题主要考虑的是如何把一个图画在平面上,使得其边与边之间产生的交叉数数目最少.图G的交叉数cr(G),是指在图G的全部画法中边与边产生的交叉的最小值.本文利用了好画法D下子图的分离圈方法,证明了两个特殊的m(≥5)阶图与n个孤立点的联图的交叉数.主要内容包括:(1)确定了图G_m~((1))与两个孤立点的联图的交叉数以及在G_m~((1))的分离圈下T~i与G_m~((1))与G_m~((1))的交叉数情况.在此基础上,利用数学归纳法和反证法,得到G_m~((1))(m≥5)与n个孤立点的交叉数.(2)分别确定了图G(2)与一个点和两个孤立点的联图的交叉数,再进一步确定在G_m~((2))的分离圈下T~i与G_m~((2))的交叉数情况.在此基础上,结合数学归纳法和反证法,得到G_m~((2))(m≥5)与n个孤立点的交叉数.
[Abstract]:The problem of crossing number of graphs is mainly concerned with how to make a picture in a plane so that the number of crossover between edges and edges is minimized. The cross number cr (G), of graph G is the minimum value of the intersection between edges and edges in all the drawing methods of graph G. In this paper, by using the separation cycle method of a well-delineated D subgraph, we prove the intersection number of two special graphs of order m (鈮，
本文编号：2160010
[Abstract]:The problem of crossing number of graphs is mainly concerned with how to make a picture in a plane so that the number of crossover between edges and edges is minimized. The cross number cr (G), of graph G is the minimum value of the intersection between edges and edges in all the drawing methods of graph G. In this paper, by using the separation cycle method of a well-delineated D subgraph, we prove the intersection number of two special graphs of order m (鈮，
本文编号：2160010
本文链接：https://www.wllwen.com/kejilunwen/yysx/2160010.html
