基于图变换的连通控制、弱凸控制和凸控制数  

Connected domination,weakly convex domination and convex domination numbers based on graph operation

作　　者：谢克莱·热不哈提 XIEKELAI·Rebuhati(School of Mathematics and Statistics,Kashi University,Kashi 844000,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000

出　　处：《山东理工大学学报（自然科学版）》2024年第5期73-78,共6页Journal of Shandong University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(12061039);新疆维吾尔自治区高校基本科研业务费科研项目(XJEDU2024P065);喀什大学校级科研项目((2023)2860)。

摘　　要：在集合D V中,对于V-D当中的每个点,至少有1个邻点在D中,则称集合D为图G的控制集,控制数是图G的阶数最小的控制集所包含的点数,所以控制参数的研究对于控制和优化系统具有重要的作用。本文研究了增加1条边对于每个点都是simpilicial点或者割点的图的弱凸控制数和凸控制数的影响,研究了增加或删除1个顶点对一般图、树图和每个点都是simpilicial点或者割点的图的控制数、连通控制数、弱凸控制数和凸控制数的影响,并给出相应的界值。A subset D V is called dominating set of graph G,if for every vertex of V-D there is at least one neighbor in D,and the domination number is the number of vertices contained in the smallest order dominating set of the graph G,so the research of control parameters plays an important role in controlling and optimizing the system.In this paper,I study the effect of adding an edge on the weakly convex domination number and convex domination number of G where every vertex of graphs is simplicial or cut-vertex.I also study the influence of adding or removing a vertex on domination number,connected domination number,weakly convex domination number and convex domination number of general graphs,tree graphs and some special graphs where every vertex of graphs is simplicial or cut-vertex,and give the corresponding boundary values.

关 键 词：控制集 弱凸控制数 凸控制数 连通控制集 

分 类 号：O157[理学—数学]