Hamilton cycles in block-intersection graphs of triple systems

Given a BIBD S = (V, B), its 1-block-intersection graph G_s has as vertices the elements of B; two vertices B₁, B₂ ∈ B are adjacent in G_s if |B₁ ∩ B₂| = 1. If S is a triple system of arbitrary index λ, it is shown that G_S is hamiltonian. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 243-246, 1999     

一类优美图

设u、ν是两个固定顶点.用b条内部互不相交且长度皆为a的道路连接u、ν所得的图用P_a,b表示.KM.Kathiresan证实P_2,2m-1(r,m皆为任意正整数)是优美的,且猜想:除了(a,b)=(2r+1,4s+2)外,所有的P_a,b都是优美的.杨元生已证实P_2r+1,2m-1是优美的,并且证实了当r=1,2,3,4时的P_2r,2m也是优美的.本文证实r=5,6,7时P_{2r,2m相似文献}   

若干图的强染色

图 G(V,E)的一正常 k-染色 σ称为 G(V,E)的 - k-强染色当且仅当对任何两个不同顶点 u和 v,只要d(u,v)≤ 2 ,则 u、v染不同颜色 (这里 d(u,v)表示 u,v之间的距离 ) ,并称 xs(G) =min{ k|存在 G的 - k-强染色 }为 G的强色数 ,本文得到 θ-图 ,Cm,n图 ,Halin图的强色数 xs(G)     

既不含4-圈又不含6-圈的平面图的非正常染色

设d₁, d₂,..., d_k是k个非负整数. 若图G=(V,E)的顶点集V能被剖分成k个子集V₁, V₂,...,V_k, 使得对任意的i=1, 2,..., k, V_i的点导出子图G[V_i] 的最大度至多为d_i, 则称图G是(d₁, d₂,...,d_k)-可染的. 本文证明既不含4-圈又不含6-圈的平面图是(3, 0, 0)-和(1, 1, 0)-可染的.     

Perfect 3-colorings on 6-regular graphs of order 9

The concept of a perfect coloring, introduced by P. Delsarte, generalizes the concept of completely regular code. We study the perfect 3-colorings (also known as the equitable partitions into three parts) on 6-regular graphs of order 9. A perfect n-colorings of a graph is a partition of its vertex set. It splits vertices into n parts A1, A2,...,An such that for all i,j∈{1,2,...,n}, each vertex of Ai is adjacent to aij vertices of Aj. The matrix A =(aij)n×n is called quotient matrix or parameter matrix. In this article, we start by giving an algorithm to find all different types of 6-regular graphs of order 9. Then, we classify all the realizable parameter matrices of perfect 3-colorings on 6-regular graphs of order 9.     

Phase transition for SIR model with random transition rates on complete graphs

We are concerned with the susceptible-infective-removed (SIR) model with random transition rates on complete graphs C _n with n vertices. We assign independent and identically distributed (i.i.d.) copies of a positive random variable ξ on each vertex as the recovery rates and i.i.d. copies of a positive random variable ρ on each edge as the edge infection weights. We assume that a susceptible vertex is infected by an infective one at rate proportional to the edge weight on the edge connecting these two vertices while an infective vertex becomes removed with rate equals the recovery rate on it, then we show that the model performs the following phase transition when at t = 0 one vertex is infective and others are susceptible. There exists λ _c > 0 such that when λ < λ _c ; the proportion r∞ of vertices which have ever been infective converges to 0 weakly as n → +∞ while when λ > λ _c ; there exist c(λ) > 0 and b(λ) > 0 such that for each n ≥ 1 with probability p ≥ b(λ); the proportion r_∞ ≥ c(λ): Furthermore, we prove that λ _c is the inverse of the production of the mean of ρ and the mean of the inverse of ξ.     

基于车身装配结构优化的改进图分解算法

在考虑车身制造和装配成本的前提下对车身装配结构优化方法进行了研究,提出一种改进的图分解算法将车身装配结构最优地分解为一组部件.以白车身侧围的装配模型为例,将结构的几何图形转化为与之对应的关系拓扑图,再分割该关系拓扑图为一组工程约束下的单连通不交叉子图集,结合遗传算法中的算子操作,利用有限单元法分析并计算得到产品几何图形的最优分割,采用NSGA-Ⅱ算法并实现该装配体综合性能最优的目标.     

基于图谱理论的纹理图像分析

图谱理论作为目前模式识别研究的热门方法之一,广泛应用于聚类与分割,但对其进行图像分析,尤其是复杂的纹理图像分析未见报道。将图谱理论引入到图像分析领域,并结合窗口纹理分析方法构造新的纹理分析算法。首先对图像灰度级进行窗口划分得到不同灰度级下的子图像,然后以各子图像作为图的顶点,子图像间的相似度作为图的边,将原图像解析为一幅带权无向图。利用图谱理论的相关思想对该无向图进行分析,可以从中获得纹理粗糙度等特征,从而完成对原始图像的分析。通过对Brodatz图像库的检索实验证明,该方法优于传统纹理分析算法。     

特殊图类的符号控制数

图G的符号控制数γS(G)有着许多重要的应用背景.已知它的计算是NP-完全问题,因而确定其上下界有重要意义.本文研究了1)一般图G的符号控制数,给出了一个新的下界;2)确定了Cn图的符号控制数的精确值.