一个围长为2且直径≤d的本原矩阵类的指数集  

On exponent set for the class of primitive matrices with girth 2 and whose diameters are not more than d

作　　者：魏海新[1] 王敏[2] 

机构地区：[1]桂林航天工业高等专科学校计算机系,广西桂林541004 [2]烟台大学数学与信息科学系,山东烟台264005

出　　处：《安徽大学学报（自然科学版）》2009年第6期21-24,共4页Journal of Anhui University(Natural Science Edition)

基　　金：广西区教育厅科研基金资助项目(桂教科研[2006]26号)

摘　　要：利用图论和数论相结合的方法,研究了围长为2的一类本原矩阵,通过有向图D的直径,给出了围长为2且直径≤d的n阶本原矩阵的本原指数的一个上确界,最后证明了围长为2且直径≤d的全体n阶本原矩阵所构成的矩阵类的本原指数集为E0d={2,3,…,3d}.By using of the combined method of graph theory and number theory,we studied the primitiveness matrices with girth 2.And it offered the least upper bound of the primitive exponent through the diameter of the infinite digraph D（A）.In the end,we proved the index set for the class of primitive matrices with girth 2 and whose diameters were not more than d was E0d={2,3,…,3d}.

关 键 词：本原矩阵 指数 围长 直径 

分 类 号：O157.5[理学—数学]