若干本原有向图类其广义本原r-指数的界  

Bounds on the Generalized r-Exponents for a Number of Primitive Digraph Classes

作　　者：黄宇飞[1] 柳柏濂[2] 

机构地区：[1]广州民航职业技术学院,广州510403 [2]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2015年第2期150-157,共8页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金数学天元基金项目(11326221)

摘　　要：k点r-指数、k点r-同位指数、第k重下r-指数和第k重上r-指数(统称为广义本原r-指数)是基于非记忆通信系统的数学模型所提出的4类有重要意义与应用背景的新指数.利用有向图的模拟、可达集的分析以及Frobenius数其有关性质的运用等方法技巧,该文主要研究了若干重要的本原矩阵(本原有向图)类其广义本原r-指数的上界估值和极矩阵(极图)刻画等问题:分别对w-不可分矩阵,w-几乎可分矩阵其k点r-指数和第k重上r-指数的上界进行了估值,并进一步刻画了完全不可分矩阵和几乎可分矩阵其k点r-指数和第k重上r-指数的上确界和极图;探讨了含多圈结构的本原有向图、含交圈结构的本原有向图其k点r-指数、k点r-同位指数、第k重下r-指数和第k重上r-指数的上界估值等问题,同时也导出了微对称本原矩阵和对称本原矩阵其4类广义本原r-指数的若干上界.Based on the mathematical model of memoryless communication system,the concepts of k-point r-exponent,k-point r-same exponent,kth lower r-multiexponent and kth upper r-multiexponent（ unified called generalized r-exponents） which are meaningful and practicable were introduced. By the techniques of imitating the digraphs,analyzing the reachable set,using the properties about Frobenius numbers,the upper bounds and extremal matrices（ digraphs） of generalized r-exponents for a number of primitive matrix（ digraph） classes are studied.Some upper bounds for the k-point r-exponent and kth upper r-multiexponent of w-indecomposable matrices and wnearly decomposable matrices are obtained respectively,and further characterize the least upper bounds and extremal digraphs for the k-point r-exponent and kth upper r-multiexponent of fully indecomposable matrices and nearly decomposable matrices. Moreover,maximum index problem for the k-point r-exponent,k-point r-same exponent,kth lower r-multiexponent and kth upper r-multiexponent of primitive digraphs with multiple cycles structure and primitive digraphs with intersecting cycles structure are discussed respectively,and some upper bounds for generalized r-exponents of micro-symmetric primitive matrices and symmetric primitive matrices are deduced.

关 键 词：本原有向图 本原矩阵 广义本原r-指数 界 

分 类 号：O151.21[理学—数学]