在结构图论中,图的哈密尔顿性的谱刻画是最具有影响力的课题之一,其主要思想是判断一个图是不是哈密尔顿图,这是NP-完全问题.因此,诸多学者对哈密尔顿性问题的研究主要集中在寻找适当的充分条件.本文借助补图的无符号拉普拉斯谱半径来刻画具有较大最小度的图的哈密尔顿性.首先,采用反证法构造了原图的闭包,将原图是否具有某性质转化到其闭包中;其次对闭包补图的结构进行了合理的分类讨论;最后分别给出了具有较大最小度的图G是哈密尔顿的,哈密尔顿-连通的以及从任意点出发可迹的关于无符号拉普拉斯谱半径的充分条件.

A path passing through all the vertices of a graph is called a Hamilton path .The graph G is said to be Hamilton-connected if any two vertices of G are connected by a Hamilton path .The graph G is traceable from any vertex if it contains a Hamilton path from every vertex of G .In terms of the edge number , the spectral radius and the signless Laplacian spectral radius of a graph ,some sufficient conditions for the graph to be Hamilton-connected and to be traceable from every vertex were presented ,respectively .

图的能量定义为其邻接矩阵所有特征值的绝对值之和.如果平衡二部图G中不同顶点族中任意两个顶点之间都有一条哈密尔顿路,则称G是哈密尔顿二部连通的.如果平衡二部图G任意删除一个大小为2P的平衡子集,所得子图仍然是哈密尔顿二部连通的,则称G是2P尔顿二部连通的.在本文中,我们用拟补图的能量给出一个平衡二部图G是2P-哈密尔顿二部连通的一个充分条件.

如果图中任意两顶点都被一条哈密尔顿路相连,则称它是哈密尔顿-连通的.本文主要利用图及其补图的Wiener指数、hyper-Wiener指数,给出了具有最小度条件的连通图是哈密尔顿-连通的充分条件.

设G=(V,E)是一个n个顶点m条边的简单无向连通图,文章通过图的谱半径和无符号拉普拉斯谱半径的界给出了一个图是泛圈图的充分条件.

设G=(V,E)为n阶简单连通图,若对每一个k(3≤k≤n),都含有长度为k的圈Ck,则称G为泛圈图.本文主要利用图及其补图的Wiener指数、hyper-Wiener指数,给出具有最小度条件的简单连通图是泛圈图的充分条件.

如果图G中任意两个顶点都被一条哈密尔顿路相连,则称G是哈密尔顿-连通的.为了得到更好的边界条件,主要利用图及a补图的Harary指数,得到具有最小度条件的连通图是哈密尔顿-连通的两个充分条件,改进了已有的相关结论.

The notion common denominator of a matrix over some number field is introduced in this paper. Some basic facts are cleared when the matrix is belonging to the special linear group over a given number field. When the integer ring of number field is a principal ideal domain, several fundamental properties on minimum common denominator are stated.

秘密的零知识证明是密码学中一个基本的方法,被广泛应用于数字签名中.文章对学者已经提出并证明的一个拥有DSA数字签名的零知识证明方案重新进行了安全性分析,并提出了一个改进的拥有DSA数字签名的零知识证明方案.该方案可以预防不拥有签名的第三方的欺骗或攻击,同时也能预防证实者的欺骗性.

It is very vital to improve the teaching quality of nu-merical analysis. In this paper, the characteristics of numerical analysis and the fault in its teaching are analyzed. Some teaching methods and teaching means on the course teaching of numerical analysis are given based on the experience of the teaching prac-tice as well.

Using the experimental data to find the function of variables is often encountered in many engineering problems.The most common known problem is the linear fit of data points.This paper presents a new algorithm for the linear fit on the base of EM algorithm which in particular solves the problem of uncertain linear fit.

The objective of this paper is to make classification of materials from a single image obtained under unknown viewpoint and illumination conditions.The problem of texture classification is solved by generating a texton dictionary based on feature vectors from filter responses first and then using two classification methodologies,nearest neighbour matching and Bayesian classification.The two algorithms are compared,and the results show that the classification accuracy of each algorithm is close to each other and both high.