关于信息图的两个问题(英文)

出度与入度均为u(≥2)的有限有向图可以视为一种传递信息的系统,人们称之为V-信息图.本文通过构造两类信息图回答了康韦和盖伊在[1]中提出的两个有关信息图的未解决问题,     

六角系统中完美匹配的覆盖与对应

本文建立了六角系统完美匹配集与覆盖集间的对应,并研究了它的一些性质。     

一类0.1矩阵变换图的边连通性

Let U (R, S) denote the class of all m×n matrices of 0's and 1's havingrow sum vector R and column sum vector S. The interchange graph G (R,S)is the graph where the vertices are the matrices in U (R, S) and where twomatrices are joined by an edge provided they differ by an interchange. Brualdishowed that the connectivity of G(R, S) is at least two. In the present paperwe prove that the edge connectivity of G(R, S) is equal to the minimum degreeof vertices of G(R, S)     

关于六角系统的Kekulé结构计数

在本文中我们给出Hesenberg矩阵的行列式的一公式，它与计算六角系统的Kekulé结构密切相关。     

Z—Transformation Graphs of perfect Matchings of Hexagonal Systems

A hexagonal system is defined to be a finit connected plane graph with no cut-vertices in which every interior region is surrounded by a regular hexagon of side length one.In the present paper we define the Z-transformation graph of a hexagonal system H to be the graph where vertices are the perfect matchings of (?) and where two perfect matchings are joint by an edge provided their symmetric difference is a hexagon of H.We prove that,if H has perfect matchings,Z(H)is a connected bipartite graph.Besides,Z(H)is either an elementary chain or a graph with girth 4.Some further results are obtained also.     

关于4—正则图的Berge猜想

我们用G=(V,E)表示简单4—正则图,v(G),ε(G)分别表示G的顶点数及棱数,即λ_(G)表示G的圈棱连通度(Cyclic edge Connectivity),λ_(G)=Min{|E′||E′E,G—E′仅由两个均含有回的连通分支构成}。若满足上述条件的E′不存在,则规定λ_(G)=ε(G)。本文中未加说明的其他记号及术语均见[1]。     

解一类线性方程组的Coates图消去方法

本文研究一类线性方程组的图论解法。此类方程组有广泛的应用。如:某些经济问题的计算,连续与离散时间马氏链平稳分布的计算,酶动力学的计算(见[6]、[12]及其所引用文献)。解此类方程组可以用支撑入树的方法,这就是著名的矩阵—树定理的推广应用。亦可用Mason图方法与Coates图方法。后2种方法是对一般的线性方程组都行之有效的。     

关于六角系统的Kekule结构计数

在本文中我们给出Ｈｅｓｅｎｂｅｒｇ矩阵的行列式的—公式，它与计算六角系统的Ｋｅｋｕｌｅ结构密切相关．     

RECOGNITION OF ESSENTIALLY DISCONNECTED BENZENOIDS

A benzenoid, or a benzenoid system, is a connected planar graph whose every interiorface is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above(resp. below) all its first neighbors. A Kekulean benzenoid is a benzenoid with at least oneperfect matching. An essentially disconnected benzenoid is a Kekulean benzenoid which hassome fixed bonds. Essentially disconnected benzenoids have proved to be very useful incertain enumeration techniques for Derfect matching. Hence the problem of recognizing     

伊凡·古德曼猜想的一个证明

本文讨论一类称为六角系统的平面图。文中未给出定义的术语均可在[3]中找到。六角系统是有限2—连通平面图,它的每个内部区域均由边长为1的正六角形围成。位于六角系统外部边界上的顶点称为六角系统的外部顶点,不是外部顶点的六角系统的顶点称为内部顶点。含有外部顶点的六角形称为外部六角形,不含外部顶点的六角形就称为