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

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.