摘要
相关文献研究了有限网络的下列颇具理论和应用价值的性质:考虑任意有限连通网络,其结点仅取"0"或"1"两种状态,开始时所有结点为"全0"状态,以后每次取定一个结点让它及其所有邻点全改变状态.该文利用数学建模成功地证明了一个与网络的大小和结构都无关的有趣结论:对任何网络经适当选取若干结点(按任意先后顺序依次)改变状态后,都能使网络从"全0"状态变为"全1"状态.且在此基础上进一步研究,给出连通网络选择点集(见定义1)的性质、树和单圈连通图选择点集的刻画、求任何连通网络全部选择点集的算法及其Matlab程序.
We considered a finite network with each vertex At the beginning of the process each vertex being in state ＂0＂, according to the following rule ： chose one vertex v each time and being in two possible statuses ： ＂1＂ or ＂0＂ later the state of the network will be changed let v and all its neighbor vertices change their states with all other vertices remaining unchanged. In the paper, we proved that if the vertices are chosen properly, then any finite networks can always be changed from the state with all vertices being in state ＂0＂ to the state with all vertices being in state ＂1 ＂. We denoted the set of the chosen vertices with this property as SCV. In this paper we investigated the properties of SCV of a network, concentrating upon two special kinds of networks corresponding to trees and connected graphs with only one circle. We also gave the algorithm of determining SCV for any connect network.
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2012年第4期1-6,共6页
Journal of Anhui University(Natural Science Edition)
基金
国家自然科学基金资助项目(10871230)
安徽大学国家大学生创新实验计划项目(101035701)
关键词
有限网络
无向图
邻接矩阵
二元域上的线性方程组
选择点集
finite network
undirected graph
adjacency matrix
linear equations in the field of twoelements
SCV（the set of the chosen vertices）
