完全图字典乘积的强半径和强直径

目前针对乘积图的强距离研究已经取得丰富成果,主要给出完全图字典乘积的强距离结果.基于字典乘积图与其因子图的关系,确定了两个完全图字典乘积的最小强半径;利用因子图与字典乘积图的顶点数的关系,得到完全图字典乘积的最大强直径和最大强半径的范围.除此之外,通过字典乘积的结合性,将字典乘积图的相关强距离结果进一步推广到多个完全图的字典乘积.     

具有给定指数的本原有向图的Hamilton性质

本文解决了１９８２年Ｊ．Ａ．Ｒｏｓｓ提出的两个问题,并得到如下结果：（１）设Ｄ是具有围长ｓ＞１和指数γ（Ｄ）＝ｎ＋ｓ（ｎ－２）的ｎ阶本原有向图,则Ｄ是Ｈａｍｉｌｔｏｎ的;（２）设Ｄ是含有环的ｎ阶本原有向图且γ（Ｄ）＝２ｎ－２,则Ｄ是Ｈａｍｉｌｔｏｎ的当且仅当ｍａｘ｛ｄ（ｕ,ｖ）|γ（ｕ,ｖ）＝２ｎ－２｝＝ｎ－２．     

常数项无穷乘积的性质及判定法

无穷乘积是研究数串级数的一种方法,在无穷乘积里极限的近似值是由反复乘新的因子形成的．本文主要讨论无穷乘积的性质及收敛的判定法．     

关于有向图代数中Lie理想的注记

本文加深了Hopenwasser和Paulsen关于有向图代数中Lie理想的一个结果,证明了有向图代数A的一个线性子空间是A的Lie理想当且仅当存在A的一个结合理想Y及A的masa D的一个子代数E,使得(Y)~0■■Y+E,其中(Y)~0是Y中迹为零的所有元的集合．     

乘积型模糊B-代数

引入乘积型模糊B-代数的概念,提供它们的几个例子,研究它们的一些性质.讨论模糊B-代数与乘积型模B-代数的关系,研究乘积型模糊B-代数的同态象与同态原象的性质,给出B-代数上乘积型模糊B-代数与B-代数的积代数上乘积型模糊B-代数的关系.     

关于交换群上的Cayley有向图的正规性

Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规,我们定出了交换群上的小度数的非正规的Cayley有向图, 并给出了一个猜想．应用这个结果,给出了pn(n≤2)个点上的度数不超过3的有向对称图的分类,这里p是一个奇素数．     

乘积误差模型的渐近性质

在较弱的条件下,从条件过程和无条件过程两个角度讨论了乘积误差模型解的渐近性质,得到了条件过程收敛于无条件过程的充分条件,任意阶矩有限的充要条件以及外生变量与内生变量持续性的充要条件.所得到的结论不但适用于已得到应用的平稳乘积误差模型,也适用于包含单位根的乘积误差模型和满足条件的其他类型的非平稳过程.     

关于Hadamard乘积矩阵的一些性质的注记

对[1]的主要结论作了说明,给出Hadamard乘积矩阵有关性质的更一般的结果。     

某些无穷乘积的代数无关性

本文研究了某些用无穷乘积定义的函数在代数点和超越点上的值的代数无关 性.     

路代数的有向图特征与Brown—McMoy根

本文解决路代数中若干遗留问题，给出本原路代数，（右）Ｇｏｌｄｉｅ路代数的有向图特征，证明广义路代数的Ｒｒｏｗｎ－ＭｃＣｏｙ根与它的Ｊａｃｏｂｓｏｎ根不必重合。     

图的字典积的非零整数流(英文)

充分利用图的字典积的结构证明了以下结论:如果图G_1的每连通分支都非平凡,图G_2的阶数大于3,那么它们的字典积G_1[G_2]具有非零3-流.     

图的笛卡儿积及字典式积的连通性

文章给出了两个图的笛卡儿积及字典式的积为最大边连通的、最大连通的、super-λ,super-κ及hyper-κ的充分条件,同时证明了其中一些条件也是必要的.此外,对这两种积的局部割集和广义割集的性质也进行了考虑.     

Lexicographic Products of Half Linearly Ordered Groups

The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4].     

On the Normality of Cayley Digraphs of Valency 2 on Non-Abelian Group of Odd Order

In this paper, we prove that the Cayley digraph = Cay(G, S) of valency 2 on non-abelian group G of odd order is normal if the automorphism group of A(), a graph constructed from by using the method presented in the paper, is primitive on the vertices set V(A(). We also prove that the Cayley digraphs of valency 2 on non-abelian group of order pq² are normal, where p and q are distinct odd primes.AMS Subject Classification (2000) 05C25 20B25Supported by the National Natural Science Foundation of China (Grant no. 19971086) and the Doctoral Program Foundation of the National Education Department of China.     

Small cycle double covers of products I: Lexicographic product with paths and cycles

Bondy conjectured that every simple bridgeless graph has a small cycle double cover (SCDC). We show that this is the case for the lexicographic products of certain graphs and along the way for the Cartesian product as well. Specifically, if G does not have an isolated vertex then G □ P₂ and G □ C_2k have SCDCs. If G has an SCDC then so does G □ P_k, k > 2 and G □ C_{2k + 1}. We use these Cartesian results to show that P_2j[G] (j ≥ 1) and C_k[G] (k ≠ 3, 5, 7) have SCDCs. Also, if G has an SCDC then so does P_{2j + 1}[G] (j ≥ 4). The results for the lexicographic product are harder and, in addition to the Cartesian results, require certain decompositions of K_n,n into perfect matchings. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 99–123, 2008     

本原对称有向图上广义指数的极图

设D是n阶有向图(允许有环但不允许有重复弧),X C V(D),集指数expD(X)是这样的最小正整数P,使得对D中每个点v,存在从X的至少一个点到V的长为P的途径.若这样的正整数P不存在,则定义expD(X)=∞.D的第k重上广义指数F(D,k):=max{expD(X)| X C V(D),|X|=k},1≤k≤n.如果F(D,k)<∞,则称D是k-上本原的.本文完全刻划了k-上本原对称有向图的第k重上广义指数的极图.     

Lexicographic product decompositions of half linearly ordered loops

In this paper we prove for an hl-loop Q an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop Q with a finite number of lexicographic factors have isomorphic refinements.     

一类非正规Cayley有向图

本文研究了2p2(p奇素数)阶非交换群上两度Cayley有向图的正规性,发现 了一无限族非正规的Cayley有向图.     

A Family of Nonnormal Cayley Digraphs

We call a Cayley digraph Γ = Cay(G, S) normal for G if G _R , the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determine the normality of Cayley digraphs of valency 2 on nonabelian groups of order 2p ² (p odd prime). As a result, a family of nonnormal Cayley digraphs is found. Received February 23, 1998, Revised September 25, 1998, Accepted October 27, 1998     

图的字典序积和自同态幺半群

Ｆ．Ｈａｒａｒｙ￣［１］和Ｇ．Ｓａｂｉｄｕｓｓｉ￣［２］考虑过图Ｘ和ｙ的字典序积Ｘ［Ｙ］的自同构群ＡｕｔＸ［Ｙ］与它们各自的自同构群的圈积ＡｕｔＸ［ＡｕｔＹ］的关系，并给出了两者相等的一种刻划．在本文，我们考虑更广意义上的问题，即Ｘ［Ｙ］的自同态幺半群ＥｎｄＸ［Ｙ］与各自的自同态幺半群的圈积ＥｎｄＸ［ＥｎｄＹ］的关系，也给出了两者相等的一种刻划，同时得到了下面结果：如果Ｘ和Ｙ都是不含Ｋ＿３导出子图的连通图，且其中之一图有奇数围长，那么ＥｎｄＸ［Ｙ］＝ＥｎｄＸ［ＥｎｄＹ］．