群与图及相关课题的研究

本综述了把群与图综合起来进行研究的一些工作,简述了与之相关的一些课题,并提出了有待解决的一些问题。     

A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems

Abstract The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke （FdV） functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems： the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = hi on Su. In the absence of body forces （Fi = 0）, it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = hi on Su can be imposed in the average sense in general and exactly if hi is linear between two contour nodes, which is obviously the case for tTi = O.     

秩$6$的无三角形的图

The rank of a graph G is defined to be the rank of its adjacency matrix A（G）. In this paper we characterize all connected triangle-free graphs with rank 6.     

关于图的3-条件色数

For integers k0,r0,a(k,r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d,r}diferent colors.The r-hued chromatic number,denoted byχr(G),is the smallest integer k for which a graph G has a(k,r)-coloring.Define a graph G is r-normal,ifχr(G)=χ(G).In this paper,we present two sufcient conditions for a graph to be 3-normal,and the best upper bound of 3-hued chromatic number of a certain families of graphs.     

集值优化问题ε-严有效解的二阶Mond-Weir对偶

在实赋范线性空间中研究带约束的集值优化在ε-严有效意义下的二阶Mond-Weir对偶问题.利用广义二阶邻接导数的性质,借助凸集分离定理得到了强对偶定理.利用ε-严有效点的性质得到了逆对偶定理.     

Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution

Let D be any division ring with an involution,Hn （D） be the space of all n × n hermitian matrices over D. Two hermitian matrices A and B are said to be adjacent if rank（A - B） = 1. It is proved that if φ is a bijective map from Hn（D）（n ≥ 2） to itself such that φ preserves the adjacency, then φ^-1 also preserves the adjacency. Moreover, if Hn（D） ≠J3（F2）, then φ preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices.     

空间计量模型中权重矩阵的类型与选择

根据空间效应产生起点及理论基础的不同,归纳了现有空间计量文献中邻接矩阵、反距离矩阵、经济特征矩阵以及嵌套矩阵等主要权重形式,并总结了其共同点、优缺点、演变脉络及使用注意事项.针对截面式权重矩阵本身面临的限制构造了两种必要的转换,即通过转换实现对不同地理区域之间空间效应的考察,以及从截面权重到面板权重的转换.最后指出研究者应该尽量采用多种新方法来确定空间权重形式以使其更客观.     

4维3元断链码的重量谱

GF(q)上[n,k;q]线性码C的重量谱为序列(d1,d2,…,dk),这里dr是C的r维子码的最小支持重量(1≤r≤k).用有限射影几何方法确定了满足含有2个邻接断点的断链条件的4维3元线性码的重量谱.     

(邻接)树图的同构及平面性

树图是非常有用的一类图.本文刻画了(邻接)树图分别为Pn,Cn,Kn的图类并且讨论了(邻接)树图的平面性.     

给定最大度的树的最大谱半径

In this paper, we characterize the trees with the largest Laplacian and adjacency spectral radii among all trees with fixed number of vertices and fixed maximal degree, respectively.