摘要
控制理论在计算机、通信等方面有很多应用。随着研究的深入,控制理论逐渐成为图论方面重要研究内容之一,全控制问题是控制理论当中的一个重要组成。通过对圆的竞赛图、圆的纯粹局部竞赛图、以及圆的非局部竞赛图三个子图类的分析,得出了圆的有向图类最小的全控制集合,进而完全刻画了其最小全控制数,并验证了Caccetta-H ggkvist猜想中全控制数的界大于等于其围长对强连通圆的有向图是紧的。
Domination theory has many applications in computer and communication.The dominating theory has gradually become one of the important research contents in graph theory.The total domination is an important component of the domination theory.Based on the analysis of round tournaments,round pure local tournaments and round non-local tournaments,the minimum total domination set of the round digraph is studied,and then the minimum total domination number is characterized completely.Finally,it is proved that the bound of the domination number in the Caccetta-H ggkvist conjecture are larger than or equal to the girth,and it is tight for a strong round digraph.
作者
张越
张新鸿
ZHANG Yue;ZHANG Xin-hong(School of Applied Sciences,Taiyuan University of Science and Technology,Taiyuan 030024,China)
出处
《太原科技大学学报》
2023年第3期274-278,284,共6页
Journal of Taiyuan University of Science and Technology
基金
山西省自然科学基金(201801D121013)
山西省优秀青年科学基金(201901D211197)。
关键词
圆有向图
竞赛图
局部竞赛图
全控制集
全控制数
round digraph
tournament
local tournament
total domination set
total domination number
