【摘要】：圖的交叉數(shù)問題主要考慮的是如何把一個圖畫在平面上,使得其邊與邊之間產(chǎn)生的交叉數(shù)數(shù)目最少.圖G的交叉數(shù)cr(G),是指在圖G的全部畫法中邊與邊產(chǎn)生的交叉的最小值.本文利用了好畫法D下子圖的分離圈方法,證明了兩個特殊的m(≥5)階圖與n個孤立點的聯(lián)圖的交叉數(shù).主要內(nèi)容包括:(1)確定了圖G_m~((1))與兩個孤立點的聯(lián)圖的交叉數(shù)以及在G_m~((1))的分離圈下T~i與G_m~((1))與G_m~((1))的交叉數(shù)情況.在此基礎(chǔ)上,利用數(shù)學(xué)歸納法和反證法,得到G_m~((1))(m≥5)與n個孤立點的交叉數(shù).(2)分別確定了圖G(2)與一個點和兩個孤立點的聯(lián)圖的交叉數(shù),再進一步確定在G_m~((2))的分離圈下T~i與G_m~((2))的交叉數(shù)情況.在此基礎(chǔ)上,結(jié)合數(shù)學(xué)歸納法和反證法,得到G_m~((2))(m≥5)與n個孤立點的交叉數(shù).
[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，

本文編號：2160010