二进制递归网络的连通性

二进制递归网络是超立方体的一类特殊变体,它具有很多良好的网络特性。网络的连通性是衡量网络结构通信能力的一个重要性能,虽然到目前为止已知的一些二进制递归网 络的连通性都已被研究过,但这些研究只是针对个体进行的,并不能代表所有二进制递归网络的连通特性。本文通过证明任何一个二进制递归网络中的每对顶点之间只能存在在”条顶点不交路,得到了整个二进制递归网络的点和边连通度皆为”的重要结论。     

BC互连网络及其性质

提出一种称为一一对应连接（BC）图的互连网络族，使其包含超立方体、交叉立方体和Mobius立方体作为基具子集，同时又使其具有与超立方体、交叉立立体和Mobius立方体相同的对数级的直径和顶点度数、最高连通（容错）度和相同的可诊断性等性质，从而使对超立方体及与其结构相似的大量互连网络的某些性质的研究合而为一，证明了BC互连网络族中包含一类Hamilton连通图并给出了BC互连网族中的图的直径的一个猜想。     

论PANCAKE互连网的连通性

本详细地讨论了ｎ－Ｐａｎｃａｋｅ在栅去不超过２ｎ－４个结点时的连通情况，并由此给出ｎ－Ｐａｎｃａｋｅ的条件连通度和条件直径，从本可以看出，ｎ－Ｐａｎｃａｋｅ是一种具有很强连通性的较好的并行网络拓扑结构。     

3元n立方网络的2阶超连通性

为了度量以3元n立方网络为底层拓扑结构的并行与分布式系统的连通性,通过构造其2阶超割的方法,计算出当n不小于2时,3元n立方网络的2阶超连通度是6n-7。证明了对于以3元n立方网络为底层拓扑结构的并行与分布式计算机系统,当有不超过6n-8个节点发生故障且每个连通分支至少还有3个健康的节点时,该并行与分布式系统的任意两个节点之间仍然有一条无故障的通信线路。     

增广泡型网络的边连通性和限制边连通性

针对泡型网络边连通度和限制边连通度小、容错能力弱的弊端,采用在泡型网络中增加通信线路的方法构建了高可靠性的增广泡型网络。通过构造最小边割的方法,证实了n维增广泡型网络中去除任意不多于n-1条边时,该增广泡型网络的任意两个节点之间依旧连通;通过构造最小限制边割的方法,证实了在不产生孤立节点的条件下,n维增广泡型网络中去除任意不多于2n-3条边时,该增广泡型网络的任意两个节点之间依旧连通。依据上述结果,通过实例证明增广泡型网络的容错能力优于泡型网络。     

LHL-立方体互连网络及其性质

并行计算系统一直是计算机科学中的重要研究领域,其互连网络的拓扑性质对整个网络的性能起着非常重要的作用.目前已经提出多种互连网络,其中超立方体具有对数级的直径、高连通度、对称性等很好的性质,故被用作多种并行机的处理器连接的拓扑结构.然而,超立方体并非所有性质都是最优的互连网络,且超立方体的许多变型结构具有许多比超立方体更好的性质,其中已经证明了局部扭立方体在直径、Hamilton连通性等方面都优于超立方体.给出在超立方体与局部扭立方体的顶点间的一种连接方式--超连接,从而得到一种称为LHL-立方体的新型网络,并对这种网络的以下性质进行了研究:顶点连通度、边连通度、Hamilton连通性、直径.研究结果表明,一个n维LHL-立方体是一个具有2n个顶点和n2n-1条边的n-正则图,n维LHL-立方体的顶点连通度和边连通度均为n,且是Hamilton连通的,直径上界为[n/2 ]+3.     

多级互连网络互连函数的矩阵理论

多级互连网网络是大规模并行处理系统和大型ＡＴＭ交换机采用的主要互连结构。     

星型网络的3-限制边连通性

星型互连网络是并行与分布式处理领域中最流行的互连网络之一,它以n维星图作为拓扑结构。k-限制边连通度是衡量网络的可靠性的参数之一。一般来说,一个网络的k-限制边连通度越大,其连通性就越好。研究了星型互连网络的k限制边连通度;证明了当n≥3时,n维星型互连网络的3-限制连通度为3n－7。     

无线传感器网络连通性研究

为优化无线传感器网络的配置参数,减少网络拓扑结构变化次数,需对其组网算法和连通性问题进行研究。从概率论角度出发研究了网络参数之间的关系,在分析了节点连通度概率分布模型后,推导出了节点通信半径、节点个数、监测区域、连通度之间的关系,并在此基础上给出了一种连通性好且节能的无线传感器网络组网算法。通过仿真实验对算法进行验证,实验结果表明使用该方法组建的无线传感器网络连通性好,有很好的应用前景。     

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Let G be a graph. Then T ⊆ V(G) is called an R^k-vertex-cut if G − T is disconnected and each vertex in V(G) − T has at least k neighbors in G − T. The size of a smallest R^k-vertex-cut is the R^k-vertex-connectivity of G and is denoted by κ^k(G). In this paper, we determine the numbers κ¹ and κ² for Cayley graphs generated by 2-trees, including the popular alternating group graphs.     

A probabilistic algorithm for vertex connectivity of graphs

A probabilistic algorithm is presented which computes the vertex connectivity of an undirected graph G = (V,E) in expected time $\text{O((-log ε|V|}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{|E|)}$ with error probability at most e provided that |E|<frcase|1/2d|V|² for some universal constant d<1.     

星网的4-限制边连通度

星网是并行与分布式处理系统中最流行的互连网络之一,它以n维星图作为拓扑结构。k-限制边连通度是衡量网络可靠性的重要参数之一;一般地,网络的k-限制边连通度越大,它的连通性就越好。研究了星网的k-限制边连通度,证明了当n≥4时,n维星网的4-限制连通度为4n－10。     

One conjecture of bubble-sort graphs

The bubble-sort graph is an important interconnection network designed from Cayley graph model. One conjecture is proposed in Shi and Lu (2008) [10] as follows: for any integer n?2, if n is odd then bubble-sort graph Bn is a union of edge-disjoint hamiltonian cycles; if n is even then bubble-sort graph Bn is a union of edge-disjoint hamiltonian cycles and its perfect matching that has no edges in common with the hamiltonian cycles. In this paper, we prove that conjecture is true for n=5,6.     

The construction of mutually independent Hamiltonian cycles in bubble-sort graphs

A Hamiltonian cycle C=? u ₁, u ₂, …, u _n(G), u ₁ ? with n(G)=number of vertices of G, is a cycle C(u ₁; G), where u ₁ is the beginning and ending vertex and u _i is the ith vertex in C and u _i ≠u _j for any i≠j, 1≤i, j≤n(G). A set of Hamiltonian cycles {C ₁, C ₂, …, C _k } of G is mutually independent if any two different Hamiltonian cycles are independent. For a hamiltonian graph G, the mutually independent Hamiltonianicity number of G, denoted by h(G), is the maximum integer k such that for any vertex u of G there exist k-mutually independent Hamiltonian cycles of G starting at u. In this paper, we prove that h(B _n )=n?1 if n≥4, where B _n is the n-dimensional bubble-sort graph.     

Conditional connectivity of Cayley graphs generated by transposition trees

Given a graph G and a non-negative integer h, the Rh-(edge)connectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. Similarly, given a non-negative integer g, the g-(edge)extraconnectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has more than g vertices. In this paper, we determine R₂-(edge)connectivity and 2-extra(edge)connectivity of Cayley graphs generated by transposition trees.