结构VAR的有向非循环图模型

研究用图模型方法辨识结构向量自回归(VAR)模型,图中的结点表示不同时刻的随机变量,结点间的边表示其所表示的随机变量之间存在的因果相依关系.针对建立有向非循环图的问题,提出了一种基于回归分析的判断方法,用回归方程的回归平方和之差作为统计量,确定当前变量之间相依关系的方向.与R ea le的逐一判别法和A lessio的图搜索方法相比,文中提出的基于统计分析的方法简单易行,且可获得唯一的当前变量有向非循环图.最后以两组模拟序列为例,验证了所提出的方法是可行且有效的.     

非h强竞赛图及其得分向量

A tournament T_n of order n is said to be h-strong if every subtournament of order n-h+1 in T_n is strong, and a score vector R_n= (r₁, r₂,… ,r_n) is said to be potentially non-h-strong if there exists some non-h-strong tournament such that its score vector is R_n. The purpose of this paper is to give a crite-rion for determining whether a score vector R_n is potentially non-h-strong.     

向量恒等式的推广

本刊2009年3月上(总365期)《数苑纵横》栏目里郭味纯老师在《一个向量恒等式及其应用》的文章中提出了一个向量恒等式(即本文定理1).本文在其基础上提出了一个更一     

向量与有向线段

作者在对中学教师进行培训的过程中 ,有几位教师提出这样的问题 :向量在人教版高中数学第一册是这样定义的 ,“我们把既有大小又有方向的量叫做向量” ,该教材同时还提到“向量常用一条有向线段来表示 ,有向线段的长度表示向量的大小 ,箭头所指的方向表示向量的方向 .”他们的问题是 ,既然向量是用有向线段来表示 ,为什么还要引入向量概念呢 ?要搞清楚这个问题 ,实质上是要弄清楚向量与有向线段间的关系 .为了彻底弄清楚 ,需要用到一点代数学的知识 .我们知道 ,如果一条线段确定了起点和终点 ,即有方向的话 ,我们就称其是一条有向线段 ,也就…     

图模型及其在统计建模中的应用

图模型是近年来兴起的一个新的统计研究方向,主要借助拓扑图的直观形式对多维概率分布进行统计推断和因果分析。本文对图模型的基本概念、原理、建模及应用进行了简单介绍。     

四类粘接图的niche数

粘接图G1(u)⊙G2(υ)是将图G1的顶点u与图G2的顶点υ重合而得到的一个图．本文证明Pm(u)⊙Kn(u是Pm的起点或终点，n≥2)，Km⊙Kn(m，n≥2)，Pm(u)⊙Cn(n≥3)和Km⊙Cn(m≥2，n≥3)这四类图都是niche图.     

一个向量恒等式及其应用

本文提出一个形式优美的向量恒等式，用它来证明斯图瓦尔特定理就显得简单而别致．让我们先复习一下有向线段A百的数量的概念：根据A白与有向直线2的方向相同或相反，分别把它的长度加上正号或负号，这样所得的数，叫作有向线段的数量，记为AB．     

3强竞赛图的得分向量

如果对n阶竞赛图T_n的每个h—1元顶点子集U,删点子图T_n—U都是强的,则称T_n是h强的。如果非降的非负整向量R_n=(r_1,r_2,…,r_n)是某个n阶h强竞赛图的得分向量,则称R_n是隐含h强的;如果所有以R_n为得分向量的n阶竞赛图都是h强的,则称R_n是完全h强的。本文给出了得分向量R_n隐含3强和完全3强的判准。     

有向循环图的同构

Let S belong to Zn-{0}.The circulant digraph DCn(S) is a directed graph with vertex set Zn and are set {(i,i s):i∈Zn,s∈S},A.Adam conjectured that DCn(S)≌DCn(T) if and only if T=uS for some unit u mod n.In this paper we prove that the conjecture is true if S is a minimal generating set of Zn and thus determine the full automorphism groups of such digraphs.The methods we employ are new and easy to be understood.     

基于有向模糊图全控制模型的多因素组合认证

与单因素身份认证相比,多因素身份认证(MFA)问题需要至少两个因素来认证实体,从而提高了信息的安全性。近年来,学者们已经对它进行了广泛的研究,并且将其应用到各个领域。本文针对多因素组合认证问题,提出了基于有向模糊图的全控制模型。首先利用有向模糊图全控制模型对多因素组合认证问题进行建模;然后使用原始对偶贪婪算法(PDGA)和基于全控制的贪婪算法(TGA)对问题进行求解;最后对两种算法的有效性进行分析,结果表明TGA算法是较有效的。     

A new method for constructing infinite families of k-tight optimal double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. DLN has been widely used in the designing of local area networks and distributed systems. In this paper, a new method for constructing infinite families of k-tight optimal DLN is presented. For k = 0,1,…,40, the infinite families of k-tight optimal DLN can be constructed by the new method, where the number nk(t,a) of their nodes is a polynomial of degree 2 in t and contains a parameter a. And a conjecture is proposed.     

图的倍图与补倍图

计算机科学数据库的关系中遇到了可归为倍图或补倍图的参数和哈密顿圈的问题．对简单图C,如果V（D（G））：V（G）∪V（G′）E（D（G））=E（C）∪E（C″）U{vivj′｜vi∈V（G）,Vj′∈V（G′）且vivj∈E（G））那么,称D（C）是C的倍图,如果V（D（G））=V（C）∪V（G′）,E（D（C））：E（C）∪E（G′）∪{vivj′}vi∈V（G）,vj′∈V（G’）and vivj∈（G））,称D（C）是G的补倍图,这里G′是G的拷贝．本文研究了D（G）和D的色数,边色数,欧拉性,哈密顿性和提出了D（G） 的边色数是D（G）的最大度等公开问题．     

图的结合数猜想的新结果

［１］中Ｗｏｏｄａｌ猜想：若图Ｇ的结合数ｂｉｎｄ（Ｇ）≥３２,则图Ｇ包含三角形,本文证明：若ｂｉｎｄ（Ｇ）≥７＋√６９１０,则图Ｇ包含三角形,从而进一步改进了［２］的结果     

A new method for constructing infinite families of k-tight optimal double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. DLN has been widely used in the designing of local area networks and distributed systems. In this paper, a new method for constructing infinite families of k-tight optimal DLN is presented. For k = 0, 1, ..., 40, the infinite families of k-tight optimal DLN can be constructed by the new method, where the number n _k (t, a) of their nodes is a polynomial of degree 2 in t and contains a parameter a. And a conjecture is proposed.     

图的星临界性

图的星着色是图的正常着色的推广。本文对图的星临界性及其与图的临界性之间的关系进行研究，给出了两类星临界但非临界的平面图。     

Balanced Graph Partitions

We prove that the set of vertices V, |V| = rk, of a connected graph G can be split into r subsets of the same cardinality in such a way that the distance between any vertex of G and any subset of the partition is at most r.     

以完全二部图作为星补的正则图的刻画

设$G$是一个$n$阶图, $\mu$是$G$的一个$(k\ge 1)$重邻接特征值. 图$G$中关于$\mu$的星补$H$是指$G$的不含特征值$\mu$的$n-k$阶诱导子图,且顶点集$X=V(G-H)$称为图$G$中关于$\mu$的星集.星补技术提供了利用部分子结构来重建满足特定性质的整个图的谱工具. 本文我们研究了关于特征值$\mu$的以$K_{t,s}~(s\ge t\ge 2)$作为是补的正则图, 特别地, 我们完全刻画了$t=3$的情形, 获得了当$t=s$时的一些性质, 并提出了有待进一步研究的问题.     

扇形图的零因子半群

Let Pn be a path graph with n vertices, and let Fn = Pn ∪ {c}, where c is adjacent to all vertices of Pn. The resulting graph is called a fan-shaped graph. The corresponding zero-divisor semigroups have been completely determined by Tang et al. for n = 2, 3, 4 and by Wu et al. for n ≥ 6, respectively. In this paper, we study the case for n = 5, and give all the corresponding zero-divisor semigroups of Fn.     

完全二部图的符号星控制数

近年来,研究图的符号星控制数颇引人注目,研究了完全二部图的符号星控制数.     

Limit points of eigenvalues of (di)graphs

The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph D, the set of limit points of eigenvalues of iterated subdivision digraphs of D is the unit circle in the complex plane if and only if D has a directed cycle. 3. Every limit point of eigenvalues of a set D of digraphs (graphs) is a limit point of eigenvalues of a set of bipartite digraphs (graphs), where consists of the double covers of the members in D. 4. Every limit point of eigenvalues of a set D of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in D. 5. If M is a limit point of the largest eigenvalues of graphs, then −M is a limit point of the smallest eigenvalues of graphs.