| 有限网络的一个性质 |
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| 引用本文： | 杨尚俊,章权兵,李红粉,王刚,张洋.有限网络的一个性质[J].数学学习,2011(4):23-27. |
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| 作者姓名： | 杨尚俊 章权兵 李红粉 王刚 张洋 |
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| 作者单位： | 安徽大学数学学院,安徽合肥230039 |
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| 基金项目： | 安徽大学国家大学生创新实验计划项目（101035701）;安徽省高等学校省级教学研究项目（2008JYXM271）. |
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| 摘 要： | 借助实例提出一个有关有限网络研究的基本问题：对装置的任意电路网络是否总能经有限次改变状态后,从全＂关闭＂状态变为全＂开启＂状态.利用无向图作为网络的数学模型,并利用邻接矩阵,可把该基本问题归结为证明二元域Z2上一个特殊的线性方程组是否有解的问题.基于二元域Z2的运算性质及此域上线性方程组的理论,可严格证明上述线性方程组...
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| 关 键 词： | 有限网络 无向图 邻接矩阵 二元域上的线性方程组 |
An Interesting Property of Finite Networks |
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| Institution: | YANG Shang-jun, ZHANU, Quan-bing, LI Hong-fen, ZHANU, Yang, WANE- Gang (School of Mathematical sciences, Anhui University, Hefei 230039, PRC) |
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| Abstract: | In this paper we give an example to present a basic problem tor finite networks： whether it is possible or not for any finite network of devices to change its status from the initial status with all its devices being in ＂close＂ state to the final status with all its devices being in ＂open＂ state？ An undirected graph whose adjacency matrix is properly defined can be used as a mathematical model of the network. We confirm the positive answer for the basic problem by proving that the corresponding system Of linear equations is consistent in the field Z_2. |
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| Keywords: | finite networks undirected graphs adjacency matrix system of linearequations in field Z_2 |
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