双对称本原矩阵k-点指数的极矩阵  

The Extremal Matrices of k-point Exponent of Doubly Symmetric Primitive Matrices

作　　者：陈佘喜[1] 曾庆光[2] 陈洁[1] 李冬梅[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201 [2]湖南大学计算机与通信学院,长沙410082

出　　处：《应用数学学报》2007年第3期486-496,共11页Acta Mathematicae Applicatae Sinica

基　　金：湖南省自然科学基金(06JJ2090);湖南省教育厅科研基金资助项目.

摘　　要：一个n阶本原矩阵A的k-点指数是A的最小幂指数,使得在这个幂中,存在着k个全1行．最近我们得到了n阶双对称本原矩阵的k-点指数的上确界．本文将在此基础上,以伴随图的形式给出其极矩阵的完全刻划．Let A be an n × n primitive matrix, and let k be an integer with 1 ≤ k ≤ n. The k-point exponent of A is the smallest power of A for which there are k rows with no zero entry. We have recently obtained the exact upper bound for the k-point exponent of doubly symmetric primitive matrices of order n with 1 ≤ k ≤ n. In this paper, we use the graph theoretical method to give a complete characterization for the extremal matrices.

关 键 词：无向图 本原矩阵 本原指数 广义指数 

分 类 号：O157.5[理学—数学]