| 一种关于图的关联矩阵秩的定理证明的新方法 |
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| 引用本文： | 陈明,李刚,蔡晓静,王向荣.一种关于图的关联矩阵秩的定理证明的新方法[J].数学的实践与认识,2012,42(9):258-262. |
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| 作者姓名： | 陈明 李刚 蔡晓静 王向荣 |
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| 作者单位： | 1. 山东科技大学信息科学与工程学院,山东青岛,266590
2. 北京工商大学数学系,北京,100048 |
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| 摘 要： | 关于图的关联矩阵的一个重要的定理是r个结点的连通图G的关联矩阵的秩是r-1.利用一般域上的线性空间理论,给出了无向图的关联矩阵秩的定理证明,该方法结构严谨且利于学生理解和接受.
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| 关 键 词： | 关联矩阵 线性空间 矩阵的秩 |
A New Proof of Theorem of the Incidence Matrix Rank in Graph |
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| CHEN Ming
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LI Gang
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CAI Xiao-jing
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WANG Xiang-rong.A New Proof of Theorem of the Incidence Matrix Rank in Graph[J].Mathematics in Practice and Theory,2012,42(9):258-262. |
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| Authors: | CHEN Ming LI Gang CAI Xiao-jing WANG Xiang-rong |
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| Institution: | 1 (1.College of Information Science and Engineering,Shandong University of Science and Technology,Qingdao 266590,China) (2.Department of Mathematics,Beijing Technology and Business University,Beijing 100048,China) |
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| Abstract: | The important theorem about the incidence matrix in graph is that the incidence matrix rank of a connected graph with r-vertex is r-1.By using the theory of linear space on a general field,this paper proposes a proof of the theorem of the incidence matrix rank in an undirected graph.This rigorous method is easy to understand and accept. |
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| Keywords: | incidence matrix linear space matrix rank |
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