循环图的Adam同构的性质

本文得到了任意两个连通循环图是(?)d(?)m同构的充要条件,并且还得到两个连通循环图是(?)d(?)m同构的另一必要条件。     

无限循环图的同构和自同构

本文证明了两个有限度的无限有向循环图Ｄ（Ｓ）和Ｄ（Ｔ）同构当且仅当Ｔ＝±Ｓ另外，还确定了有限度的无限（有向）循环图的全自同构群     

张量乘积图的同构因子分解

本文讨论了两个可分图的张量乘积图的同构因子分解问题.给出了张量乘积图可同构因子分解的判定条件.     

几类图张量乘积的同构因子分解

对任意给定的正整数ｔ，当ｔ能整除图Ｇ的边数时．Ｇ就可分解成ｔ个同构的生成子图，则称Ｇ为可分图．本文证明了路、圈的张量乘积，以及可分图与路、圈的张量乘积仍然是可分图．此外，文中讨论了完全图张量积乘的同构因子分解．     

Cayley图的同构分解及弱DCI-子集的充要条件

本文得到了Ｃａｙｌｅｙ图的同构分解定理及弱ＤＣＩ－子集的充要条件．证明了二面体群是弱２－ＤＣＩ－群，同时确定了二面体群上２度Ｃａｙｌｅｙ图的自同构群．     

二面体群的小度数Cayley图的同构类的计数

设G是有限群,S是G的一个不包含单位元的非空子集且满足S^-1=S,定义群G关于S一个的Cayley图x=Cay(G,S)如下：V(X)=G,E(X)=｛(g,sg)｜g∈G,s∈S}.对于素数P,本文给出了2p阶的二面体群的3度和4度Cayley图的同构类的个数.     

项链李代数的同构与同构群

研究了一些特殊箭图的同构,这些特殊箭图包括垂直叠加的箭图和水平叠加的箭图. 跟以前的研究方法相比, 文中的研究方法是不同的和新颖的, 即利用指标数组把复杂的李运算转换为多重指标集的运算.     

关于正项级数敛散性判定的一类方法

判定正项级数∑n=1an的敛散性,当达朗贝尔或柯西判别法失败后,可用本文提供的方法判定敛散性.     

病态线性方程组的判定方法

针对用条件数来衡量方程组的性态将随阶数增大而变得异常困难这一问题,分析了病态线性方程组产生的原因,提出了一种判定方法,探讨了对一定精度要求的解的可允许扰动的数量级,实例证明了这种方法的有效性.     

When Are Covers Relative to Two Classes Isomorphic

Let ?₁ ? ?₂ be classes of right R-modules, we introduce ?₁-covering modules and projective modules relative to ?₂ to characterize the relations between the existences of ?₁-covers, ?₂-covers and the classes ?₁, ?₂. As corollaries, every module in ? _n is an ?-covering module if and only if every flat cover is an ? _n -cover for each right module if and only if R is a von Neumann regular ring whenever wD(R) < ∞; every flat right R-module is projective relative to 𝒫 if and only if every flat cover is a projective cover for each right module if and only if R is right perfect.     

Spectral Characterizations of Some Distance-Regular Graphs

When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2,1), (3,1) and (4,1), the Biggs-Smith graph, the M ₂₂ graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.     

一类直径为2的极大平面图的Mostar指数

图G的Mostar指数定义为Mo(G)=∑uv∈Ε(G)|nu-nv|,其中nu表示在G中到顶点u的距离比到顶点v的距离近的顶点个数,nv表示到顶点v的距离比到顶点u的距离近的顶点个数.若一个图G的任两点之间的距离至多为2,且不是完全图,则称G是一个直径为2的图.已知直径为2点数至少为4的极大平面图的最小度为3或4.本文研究了直径为2且最小度为4的极大平面图的Mostar指数.具体说,若G是一个点数为n,直径为2,最小度为4的极大平面图,则(1)当n≤12时,Mostar指数被完全确定;(2)当n≥13时,4/3n2-44/3n+94/3≤Mo(G)≤2n2-16n+24,且达到上,下界的极图同时被找到.     

Bicolored Matchings in Some Classes of Graphs

We consider the problem of finding in a graph a set R of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with n nodes on each side, we give sufficient conditions for the existence of a set R with |R|=n+1 such that perfect matchings with k red edges exist for all k,0≤k≤n. Given two integers p<q we also determine the minimum cardinality of a set R of red edges such that there are perfect matchings with p red edges and with q red edges. For 3-regular bipartite graphs, we show that if p≤4 there is a set R with |R|=p for which perfect matchings M_k exist with |M_k∩R|≤k for all k≤p. For trees we design a linear time algorithm to determine a minimum set R of red edges such that there exist maximum matchings with k red edges for the largest possible number of values of k.     

Some Elementary Ramanujan Graphs

We give elementary constructions of two infinite families of Ramanujan graphs of unbounded degree. The first uses the geometry of buildings over finite fields, and the second uses triangulations of modular curves.Mathematics Subject Classiffications (2000). Primary: 05C25; secondary: 05C50, 51E24     

若干并图的优美标号

证明了,对任意大于1的自然数m,n,p,非连通图(■ V ■)∪K_(n,p)是优美图;当k≤p,m=kn+3或m=kn+1时,非连通图(P_2 V ■)∪K_(n,p)是优美图;当p≥2,m=3k+1时,非连通图(P_2 V ■)∪K_(3,p)是优美图;对任意正整数n,p,非连通图(P_1 V P_(2n+2))∪_(n,p)是优美图.     

Isomorphic Cayley graphs on nonisomorphic groups

The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended. © 1999 John Wiley & Sons, Inc. J Graph Theory 3: 345–362, 1999     

若干笛卡尔积图的邻点可区别E-全染色

图G(V,E)的k是一个正整数,f是V(G)∪E(G)到{1,2,…,k}的一个映射,如果u,v∈V(G),则f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv),C(u)≠C(v),称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数.得到了Pm×Pn,Pm×Cn,Cm×Cn的邻点可区别E-全色数,其中C(u)={f(u)}∪{f(uv)uv∈E(G)}.     

Biclique-Helly Graphs

A graph is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly graphs, leading to polynomial time recognition algorithms. In addition, we relate biclique-Helly graphs to the classes of clique-Helly, disk-Helly and neighborhood-Helly graphs.     

结构刚度函数识别的一个途径

为了计算结构的刚度函数,将结构振动微分方程分解为关于已知的原始刚度函数的微分方程和关于未知待求的刚度函数的第一类Fredholm积分方程,利用p个光滑因子进行外插值的求解方法,数值计算当光滑因子为零时的积分方程的稳定解．从而可得到结构的刚度函数．通过数值模拟说明方法是可行的．