λ型传递矩阵与多因素模糊决策

基于已知常用的模糊矩阵传递性概念定义了λ型传递。给出了它的几个等价条件。研究它的图论特征，指出λ型传递矩阵的圈都过强对边二元圈。随后证明了与全传递模糊矩阵的等价性。进一步研究与截矩阵的性质一致问题，证明了λ型传递满足一致性。最后给出λ型传递在模糊排充中的应用，表明它是一种新的实用的多因素模糊决策的数学模型。     

图论中矩阵的可实现性

对图的关联矩阵,邻接矩阵,基本割集矩阵,基本圈矩阵的可实现性分别进行了论证,并将邻接矩阵的可实现性推广到一般形式.得到了同一个基本割集矩阵的奥凯达图形是不唯一的;以及这些奥凯达图形所对应的图是互相同构的结果;并且指出了基本圈矩阵的可实现性可以依靠基本割集矩阵的可实现性来解决.     

具有$2$为无符号拉普拉斯特征值的完美匹配单圈图

本文给出了$2$为完美匹配单圈图的无符号拉普拉斯特征值的充分必要条件.     

关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

一类圈积的自同构群的矩阵描述

使用Bidwell和Curran在2006年引入的描述半直积的自同构的矩阵方法,结合作者等人在2010年证明的关于稳定自同构群的矩阵公式,得到了一类正则圈积的自同构群的矩阵描述,并求出了自同构群的阶.     

带弦有向圈的2级合成

考察带一条弦的有向圈的2级合成图,得到了它们强连通的充要条件,这些结果被用于判定布尔矩阵组合合成的本原性。     

网络最小树的一种矩阵算法

求网络最小树问题，人们熟知常用的方法有“避圈法”和“破圈法”，这些方法有其直观易解的优点，然而它们毕竟是要在图上作业（在图上完成）。由于网络与距离矩阵的对应关系，本文将利用矩阵性质给出该问题的一个矩阵解法。     

恰有t行含s圈正元的布尔矩阵幂敛指数的估计

设D_n,s(t)是恰有t行含s圈正元的n阶布尔矩阵的集合,本文得到了当s为素数时D_n,s(t)中矩阵的幂敛指数的一个新上界。     

k-控制阵

给出k-控制阵的定义,讨论k-控制阵与k-圈控制阵的关系,指出k-控制阵的周期是k的一个因子,指数不大于(n-1)k m.     

新单圈图H(p,tK_(1,m))的拉普拉斯谱刻画

设图H(p,tK_(1,m))是一个顶点数为p+mt的连通单圈图,它是由圈C_p的依次相邻的t(1≤t≤p)个顶点的每一个顶点分别与星K_(1,m)的中心重合而得到的单圈图.现证明单圈图H(p,pK_(1,5)),H(p,(p-1)K_(1,4))是由它们的拉普拉斯谱确定的,并证明了当p为偶数时,单圈图H(p,2K_(1,4)),H(p,(p-2)K_(1,4)),H(p,(p-3)K_(1,4))也是由它们的拉普拉斯谱确定的.     

正圆有向图中的弧不相交的Hamilton路和圈

2012年,Bang-Jensen和Huang(J.Combin.Theory Ser.B.2012,102:701-714)证明了2-弧强的局部半完全有向图可以分解为两个弧不相交的强连通生成子图当且仅当D不是偶圈的二次幂,并提出了任意3-强的局部竞赛图中包含两个弧不相交的Hamilton圈的猜想.主要研究正圆有向图中的弧不相交的Hamilton路和Hamilton圈,并证明了任意3-弧强的正圆有向图中包含两个弧不相交的Hamilton圈和任意4-弧强的正圆有向图中包含一个Hamilton圈和两个Hamilton路,使得它们两两弧不相交.由于任意圆有向图一定是正圆有向图,所得结论可以推广到圆有向图中.又由于圆有向图是局部竞赛图的子图类,因此所得结论说明对局部竞赛图的子图类――圆有向图,Bang-Jensen和Huang的猜想成立.     

有向圈的行列式算法及HAMILTON图条件

本文引入有向路乘法、弧行列式等概念 ,讨论了弧行列式的性质 ,阐述了二种计算有向圈的行列式方法及有向图 D为 Hamilton图的充要条件 ,最后给出了计算实例     

(p,q)-odd digraphs

A digraph D is (p,q)-odd if and only if any subdivision of D contains a directed cycle of length different from p mod q. A characterization of (p,q)-odd digraphs analogous to the Seymour-Thomassen characterization of (1, 2)-odd digraphs is provided. In order to obtain this characterization we study the lattice generated by the directed cycles of a strongly connected digraph. We show that the sets of directed cycles obtained from an ear decomposition of the digraph in a natural way are bases of this lattice. A similar result does not hold for undirected graphs. However we construct, for each undirected 2-connected graph G, a set of cycles of G which form a basis of the lattice generated by the cycles of G. © 1996 John Wiley & Sons, Inc.     

回路1、2-弦图的逆M矩阵完备及其算法设计

对已定元均不为零的部分逆M矩阵,通过变换使其对角线上元素均为1后,根据其所对应图形的特点,得到结果如下:(a)若其所对应图形为简单有向回路或回路1-弦图,具有逆M矩阵完备式当且仅当所有简单有向回路的回路积均小于1.(b)若其所对应图形为回路2-弦图,具有逆M矩阵完备式当所有简单有向回路满足回路积小于1,且对其中依次在两个顶点处相交的有向回路标明层次后,任一有向回路的回路积均小于与其相连接的上一层的有向回路的回路积.     

The Twin Domination Numb er of Strong Pro duct of Digraphs

Let γ*(D) denote the twin domination number of digraph D and let D_1  D_2 denote the strong product of D_1 and D_2. In this paper, we obtain that the twin domination number of strong product of two directed cycles of length at least 2.Furthermore, we give a lower bound of the twin domination number of strong product of two digraphs, and prove that the twin domination number of strong product of the complete digraph and any digraph D equals the twin domination number of D.     

Cycle factors in strongly connected local tournaments

A digraph without loops, multiple arcs and directed cycles of length two is called a local tournament if the set of in-neighbors as well as the set of out-neighbors of every vertex induces a tournament. A digraph is 2-connected if the removal of an arbitrary vertex results in a strongly connected digraph.In 2004 and 2005, Li and Shu investigated the structure of strongly connected, but not 2-connected tournaments. Using their structural results they were able to give sufficient conditions for a strongly connected tournament T to have complementary cycles or a k-cycle factor, i.e. a set of k vertex disjoint cycles that span the vertex set of T.Inspired by the articles of Li and Shu we develop in this paper the structure necessary for a strongly connected local tournament to be not cycle complementary. Using this structure, we are able to generalize and transfer various results of Li and Shu to the class of local tournaments.     

Planar Digraphs of Digirth Five Are 2‐Colorable

Neumann‐Lara (1985) and ?krekovski conjectured that every planar digraph with digirth at least three is 2‐colorable, meaning that the vertices can be 2‐colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2‐colorable. The result also holds in the setting of list colorings.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

On even factorizations and the chromatic index of the Kautz and de Bruijn digraphs

Motivated by the problem of designing large packet radio networks, we show that the Kautz and de Bruijn digraphs with in- and outdegree d have arc-chromatic index 2d. In order to do this, we introduce the concept of even 1-factorizations. An even 1-factor of a digraph is a spanning subgraph consisting of vertex disjoint loops and even cycles; an even 1-factorization is a partition of the arcs into even 1-factors. We prove that if a digraph admits an even 1-factorization, then so does its line digraph. (In fact, we show that the line digraph admits an even 1-factorization even under a weaker assumption discussed below.) As a consequence, we derive the above property of the Kautz and de Bruijn digraphs relevant to packet radio networks. © 1993 John Wiley & Sons, Inc.     

Note on a min‐max conjecture of Woodall

In 1978 Woodall [ 6 ] conjectured the following: in a planar digraph the size of a shortest cycle is equal to the maximum cardinality of a collection of disjoint tranversals of cycles. We prove that this conjecture is true when the digraph is series‐parallel. In fact, we prove a stronger weighted version that gives the latter result as a corollary. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 36–41, 2001