单圈图Z_4生成的凯莱图CZ_4在MM~*模型下的1好邻诊断度

多处理系统的诊断度是一个重要的研究课题.一种新的系统故障诊断方法称为g好邻诊断度,它是限制每个无故障点至少包含g个无故障的邻点.证明了单圈图Z_4生成的凯莱图CZ_4在MM~*模型下的1好邻诊断度是6.     

具有最大度距离的单圈图

设U (n)是具有n个顶点的所有单圈图的集合,G(3; n- 3)是由一个三角形C3粘上一条悬挂路P_(n-3)得到的单圈图.本文将证明当n 5时具有最大度距离的单圈图是G(3; n - 3).     

Bubble-sort网络的连通度和超连通度

Bubble-sort网络Bn是(n-1)-正则,点传递的二部图.在这篇文章中,我们确定了当n≥2时,Bn的(边)-连通度为n-1;当n≥3时,Bn的超(边)-连通度为2n-4.     

关于Mbius立方体网格的连通度(英文)

图的连通度、超连通性和限制连通度是度量互连网络容错性的重要参数 .该文考虑n维M bius立方体网络MQn,证明了它的点和边连通度都为n ,当n是任何正整数时它是超连通的 ,当n≠ 2时它是超边连通的 ,当n≥ 3时它的限制点连通度和当n≥ 2时的限制边连通度都为 2n- 2 .     

平衡立方体的h-额外连通度及h-额外条件诊断数

互连网络的连通度和可诊断数是衡量网络性能优劣的经典参数.h-额外连通度作为连通度的一种推广,是度量互连网络可靠性的一个重要指标.相应地,h-额外条件诊断数作为传统可诊断度的推广,也是度量系统诊断能力的一种新的性能指标.另外,平衡立方体网络作为超立方体网络的变形,在保留前者原有优良性能的基础上,又增加了一些新的优良性能.文中确定了平衡立方体(BH_n)的4-额外连通度和5-额外连通度都是6n-8.在此基础上,进一步推导出当h=4,5,n≥4时,BH_n在PMC模型下的h-额外条件可诊断数是6n-3.从而表明了在h-额外条件诊断策略下的可诊断数几乎是传统可诊断数的3倍.     

一道数列例题的改编——由前n项和Sn推导通项公式an

原题(人教A版必修5 P44例3) 已知数列{an}的前n项和Sn=n2+1/2n,求数列的通项公式an. 解:当n≥2时,an=Sn-Sn-1=(n2+1/2n)-[(n-1) 2+1/2(n-1)]=2n-1/2. 当n-1时,a1=S1=3/2,也适合an=2n-1/2, 所以an=2n-1/2. 分析:(1)教材目的是把握an与Sn的关系,学会通过S推导通项公式an={S1,n=1,Sn-Sn-1,n≥2.     

完全对换网络的限制连通度

完全对换网络是基于 Cayley 图模型的一类重要互连网络. 一个图 G 的 k-限制点(边)连通度是使得 G-F 不连通且每个分支至少有 k 个顶点的最小点(边)子集 F 的基数, 记作 \kappa_{k}(\lambda_{k}). 它是衡量网络可靠性的重要参数之一, 也是图的容错性的一种精化了的度量. 一般地, 网络的 k-限制点(边)连通度越大, 它的连通性就越好. 证明了完全对换网络 CT_{n} 的 2-限制点(边)连通度和 3-限制点(边)连通度, 具体来说: 当 n\geq4 时, \kappa_{2}(CT_{n})=n(n-1)-2, \kappa_{3}(CT_{n})=\frac{3n(n-1)}{2}-6; 当 n\geq3 时, \lambda_{2}(CT_{n})=n(n-1)-2, \lambda_{3}(CT_{n})=\frac{3n(n-1)}{2}-4.     

常曲率空间中具正Ricci曲率的子流形

设S~(n+p)(1)是一单位球面,M~n是浸入S~(n+p)(1)的具有非零平行平均曲率向量的n维紧致子流形.证明了当n≥4,p≥2时,如果M~n的Ricci曲率不小于(n-2)(1+H~2),则M~n是全脐的或者M~n的Ricci曲率等于(n-2)(1+H~2),进而M~n的几何分类被完全给出.     

U-统计量的一些强极限定理的精确渐近性

设{Xn;n≥1}是一列i.i.d.随机变量序列,Un是以对称函数h(x,y)为核函数的U-统计量.记Un=2n(n-1) 1≤i相似文献   

可迁图的超常边连通度的最优性

图的超常边连通度是图的边连通度概念的推广.对于n阶点可迁或正则边可迁的简单连通图来说,它的h阶超常边连通度λh一定存在(1≤h≤n/2).本文证明了当dr正则的n-阶点可迁简单连通图满足n≥6,d≥4且围长g≥5时,或d-正则的n-阶边可迁简单连通图满足n≥6,d≥4且围长g≥4时,对于任何的h1≤h≤min{g-1,n/2},λh达到其最大可能值,即λh=hd-2(h-1).     

DIAGNOSABILITY OF CAYLEY GRAPH NETWORKS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS MODEL

Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay(T_n,S_n) generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system.In this paper,it is proved that diagnosability of Cay(T_n,S_n) is n-1 under the comparison diagnosis model for n ≥ 4.     

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.     

定向图的斜秩

定向图Gσ是一个不含有环(loop)和重边的有向图,其中G称作它的基图.S(Gσ)是Gσ的斜邻接矩阵.S(Gσ)的秩称为Gσ的斜秩,记为sr(Gσ).定向图的斜邻接矩阵是斜对称的,因而,它的斜秩是偶数.本文主要考虑简单定向图的斜秩,首先给出斜秩的一些简单基本知识,紧接着分别刻画斜秩是2的定向图和斜秩是4的带有悬挂点的定向图;其次利用匹配数给出具有n个顶点、围长是k的单圈图的斜秩表达式;作为推论,列出斜秩是4的所有单圈图和带有悬挂点的双圈图;另外研究具有n个顶点、围长是k的单圈图的图类中斜秩的最小值,并刻画了极图;最后研究斜邻接矩阵是非奇异的定向单圈图.     

Almost all Cayley graphs are hamiltonian

It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph. In spite of the difficulty in proving this conjecture, we show that almost all Cayley graphs are hamiltonian. That is, as the order n of a groupG approaches infinity, the ratio of the number of hamiltonian Cayley graphs ofG to the total number of Cayley graphs ofG approaches 1.Supported by the National Natural Science Foundation of China, Xinjiang Educational Committee and Xinjiang University.     

Graphs that admit square 1-factorizations are hamiltonian Cayley graphs

A square 1-factorization of a graph is a 1-factorization in which the union of any two distinct 1-factors is a disjoint union of 4-cycles. We show that a graph admits a square 1-factorization if and only if it is a Cayley graph with group (₂) ⁿ for somen. The rest of the title follows since Cayley graphs of abelian groups are known to be hamiltonian.     

Some results on the ordering of the Laplacian spectral radii of unicyclic graphs

A unicyclic graph is a graph whose number of edges is equal to the number of vertices. Guo Shu-Guang [S.G. Guo, The largest Laplacian spectral radius of unicyclic graph, Appl. Math. J. Chinese Univ. Ser. A. 16 (2) (2001) 131–135] determined the first four largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. In this paper, we extend this ordering by determining the fifth to the ninth largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices.     

Optimally super-edge-connected transitive graphs

Let X=(V,E) be a connected regular graph. X is said to be super-edge-connected if every minimum edge cut of X is a set of edges incident with some vertex. The restricted edge connectivity λ′(X) of X is the minimum number of edges whose removal disconnects X into non-trivial components. A super-edge-connected k-regular graph is said to be optimally super-edge-connected if its restricted edge connectivity attains the maximum 2k−2. In this paper, we define the λ′-atoms of graphs with respect to restricted edge connectivity and show that if X is a k-regular k-edge-connected graph whose λ′-atoms have size at least 3, then any two distinct λ′-atoms are disjoint. Using this property, we characterize the super-edge-connected or optimally super-edge-connected transitive graphs and Cayley graphs. In particular, we classify the optimally super-edge-connected quasiminimal Cayley graphs and Cayley graphs of diameter 2. As a consequence, we show that almost all Cayley graphs are optimally super-edge-connected.     

Induced cayley graphs and d0ouble covers

Motivated by a construction of highly expanding simple Cayley graphs of dihedral groups derived from-or induced by-highly expanding Cayley digraphs fo cyclic groups presented by F. R. K. chung, constructions of simple Cayley graphs on a semidirect product of groups and Cayley digraphs of one of its factors are suggested. In case of the non-normal factor being the cyclic group of order 2. a condition is given to derive spectral bounds of the Cayley graph of the product from those of the Cayley graph of the normal factor.     

The Laplacian spread of quasi-tree graphs

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. Bao, Tan and Fan [Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011-1015.] characterize the unique unicyclic graph with maximum Laplacian spread among all connected unicyclic graphs of fixed order. In this paper, we characterize the unique quasi-tree graph with maximum Laplacian spread among all quasi-tree graphs in the set Q(n,d) with .