摘要
分别讨论了n阶无向圈图的关联矩阵和n阶有向圈图的关联矩阵、邻接矩阵的行列式、秩等代数性质,并得到相应的结论:(1)n阶无向圈图的关联矩阵M(C_n)的行列式与秩分别为:|M(C_n)|={2,n为奇数0,n为偶数,R(M(C_n))={n,n为奇数n-1,n为偶数;(2)n阶有向圈图的关联矩阵M(Cn)的行列式与秩分别为:n∈Z,都有|M(C_n)|=0,R(M(C_n))=n-1;(3)n阶有向圈图的邻接矩阵A(C_n)的行列式与秩分别为:|A(Cn)|={1,n为奇数-1,n为偶数,R(A(C_n))=n,n∈Z.
In this paper,we discuss the correlation matrix of n order undirected graph and the correlation matrix of order directed graph,the determinant of adjacency matrix,the algebraic properties of rank and so on,and get the corresponding conclusion: 1 the determinant and rank of the correlation matrix M( Cn) of n order undirected graphs are: | M( Cn) | = 2,R( M( Cn)) = n,n is odd; | M( Cn) | = 0,R( M( Cn)) = n-1,n is even.2 The determinant and rank of the correlation matrix M( Cn) of n order directed graph are: | M( Cn) | = 0,R( M( Cn)) = n-1,n is integer. 3 The determinant and rank of the adjacency matrix A( Cn) of the directed graph are: | A( Cn) | = 1,R( A( Cn) = n,n is odd; | A( Cn) | =-1,R( A( Cn)) = n,n is even.
出处
《湖北民族学院学报(自然科学版)》
CAS
2016年第3期295-298,共4页
Journal of Hubei Minzu University(Natural Science Edition)
基金
国家自然科学基金项目(11661023)
2015年省级本科教学工程建设项目(黔教高发[2015]337号)
关键词
圈图
关联矩阵
邻接矩阵
行列式
秩
circle graph
incidence matrix
adjacency matrix
determinant
rank