玫瑰花窗图R_3k+2(1,3)的交叉数

The Crossing Number of Rose Windows Graph R_3k+2(1,3)

摘要: 图论是离散数学的一个重要分支，是一门研究图的学问，而图的交叉数也是图论中的一个重要的研究方向，国内外诸多学者都对图的交叉数问题展开了相关研究。玫瑰花窗图是广义周期图的一类延伸，本文针对玫瑰花窗图的交叉数展开研究，给出了玫瑰花窗图R_3k+2(1,3)的相关定义，找到了R_3k+2(1,3)的一个好的画法，得到了R_3k+2(1,3)的交叉数的上界。最后利用数学归纳法和反证法得到了玫瑰花窗图R_3k+2(1,3)的交叉数的下界，进而完成了证明。

Abstract: Graph theory is an important branch of discrete mathematics, which is a study of graphs, and the crossing number of graphs is also an important research direction in graph theory. This paper studies the crossing number of the rose windows graph, gives the relevant definition of R_3k+2(1,3) the of the rose windows graph, finds a good drawing of R_3k+2(1,3) , and obtains the upper bound of the crossing number of R_3k+2(1,3) . Finally, the lower bound of the crossing number of the rose windows graph R_3k+2(1,3) is obtained by using the mathematical induction method and the counterproof method, and then the proof is completed.