相对于Wiener-Hosoya指标的最小树

Wiener-Hosoya指标是由Randic在文[1]中引入的一个指标,旨在揭示分子结构与其化学性质的更进一步的关系.任意给定点数及直径,本文确定了相对于该指标的最小树.进一步地,具有任意给定点数的最小的16个树也得到确定.     

树网络上f模式最优广播问题的线性算法

网络G的一个结点v上的一次广播是指从它将一个消息传递给若干相邻结点.所谓f模式广播,是指结点v在一次广播中至多向f(v)个相邻结点传递信息(f为给定的整值函数).假定每一次广播的执行时间为一单位.网络G的广播过程是广播的时间安排,使所有结点均获得消息.最优广播问题是求总时间最少的广播过程.在G是树网络情形,文献中已给出时间界为O(n2)的算法.本文给出线性时间的简捷算法.     

高功率多程放大系统中鬼像的分析

为了有效地避免鬼像破坏,针对采用离轴多程放大的高功率固体激光实验装置的光路特点,利用“光路二叉树”原理和“矩阵光学”方法,将全光路“单元化”为主放大、助推放大、反转器和输出4个部分进行光线追迹和鬼像分析,给出了各个部分的主要鬼像分布.并通过将鬼像分析的结果与前期实验中发现的现象进行比对,证明了此种分析方法的可行性和可靠性.从而为在今后实验装置的改造和类似系统的设计中有效的分析和规避鬼像提供了理论和实验依据.     

直径为4的树的奇强协调性

对简单图G=〈V,E〉,如果存在一个映射f:V→{0,1,2,…,2 E-1}满足1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=f(u)+f(v),e=uv;3){g(e)e∈E}={1,3,5,…,2 E-1},则称G为奇强协调图,f称为G的奇强协调标号.给出了直径为4的树的奇强协调标号.     

On the chromatic spectrum of acyclic decompositions of graphs

If G is any graph, a G‐decomposition of a host graph H = (V, E) is a partition of the edge set of H into subgraphs of H which are isomorphic to G. The chromatic index of a G‐decomposition is the minimum number of colors required to color the parts of the decomposition so that two parts which share a node get different colors. The G‐spectrum of H is the set of all chromatic indices taken on by G‐decompositions of H. If both S and T are trees, then the S‐spectrum of T consists of a single value which can be computed in polynomial time. On the other hand, for any fixed tree S, not a single edge, there is a unicyclic host whose S‐spectrum has two values, and if the host is allowed to be arbitrary, the S‐spectrum can take on arbitrarily many values. Moreover, deciding if an integer k is in the S‐spectrum of a general bipartite graph is NP‐hard. We show that if G has c > 1 components, then there is a host H whose G‐spectrum contains both 3 and 2c + 1. If G is a forest, then there is a tree T whose G‐spectrum contains both 2 and 2c. Furthermore, we determine the complete spectra of both paths and cycles with respect to matchings. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 83–104, 2007     

Construction of universal one-way hash functions: Tree hashing revisited

We present a binary tree based parallel algorithm for extending the domain of a universal one-way hash function (UOWHF). For t?2, our algorithm extends the domain from the set of all n-bit strings to the set of all ((2^t-1)(n-m)+m)-bit strings, where m is the length of the message digest. The associated increase in key length is 2m bits for t=2; m(t+1) bits for 3?t?6 and m×(t+⌊log₂(t-1)⌋) bits for t?7.     

A decision-theoretic approach to robust optimization in multivalued graphs

This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenarios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach.     

完全区间树顶点数目的大数律

本文讨论完全区间树顶点数目Sx的大数律,所采用的方法不同于单边区间树．文章包括三部分内容:首先探讨完全区间树所得以定义的概率空间,弄清楚它的结构,为强大数律的研究奠定理论基础．接着,针对完全区间树上的Sx的矩母函数不易求得的情况,另辟蹊径,求得Sx的期望和方差．最后,给出Sx的强弱大数律．     

On the Monotonicity of the Speed of Random Walks on a Percolation Cluster of Trees

The authors consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of trees. A sufficient condition is established for Galton-Watson trees.