关于加权距离正则图和立方图

令G=(V,E)是简单的连通k-正则图;w_1相似文献   

关于一类立方图的可连通性

文献[1]中提出阶为n(n≥3)的路的立方图是可圈图当且仅当n为奇数,本文主要证明阶为n(n≥3)的路的立方图是可连通图当且仅当n为奇数,从而加强了文献[1]中的结论.     

SAS软件在质量管理中的应用

本文介绍了质量控制的常用方法及其在ＳＡＳ软件中的实现     

一国两制育紫荆 荣归十年红东方——献“十行纵横（幻）图”贺香港回归十周年

10~2=10×10=100(百子),将1至100的自然连续数不重不漏地组合排列入纵与横各10格的方形里,要求它的纵、横、斜(两对角,下同)各自之和都相等而构成百子纵横图:     

立方图的对控制数

设G=(V,E)是一个简单图, 对任意的顶点子集合 $S\subseteq V$, G[S]表示图G中由S所导出的子图. 如果S是G的一个控制集并且G[S]包含至少一个完备匹配, 则称S是G的一个对控制集. G中对控制集的最少的顶点数称为$G$的对控制数, 记为γ_p(G). 该文证明了对任意有n点的连通立方图G, γ_p(G)≤3n/ 5.     

素数立方阶群局部传递的图

目的是研究局部传递图的性质和分类.运用置换群和陪集图的理论,获得了关于素数立方阶群局部传递图的完全分类,证明了这些图是一些互不相交的关于素数立方阶群边传递图的并.     

降低仪表板表面褶皱缺陷率的模糊集合论方法

揭示汽车饰件之一的仪表板表面褶皱缺陷应用模糊集合表征的合理性和必要性，提出应用模糊排列图的方法寻找产生仪表板表面褶皱的原因，这一方法由于具有λ-截集累积分析和动态分析的特点，对于缺陷原因的确定更具科学性，本文为模糊排列图的应用提供了一个具有说服力的案例。     

有限素数度弧正则图

如果一个图的全自同构群在其弧集上正则,则称此图为弧正则图.本文刻画素数度的立方自由阶弧正则图,证明任何素数度2倍奇立方自由阶弧正则图都是正规或二部正规Cayley图,且不存在任意素数度4倍奇立方自由阶的弧正则图,推广了一些已知的结果,得到阶为8倍奇平方自由阶素数度弧正则图的分类,并发现新的弧正则图类.此外,基于所得的结果,我们提出一个猜想和有待后续研究的一些问题.     

子立方无爪图的单射边色数至多为6

设$G$是一个图. 图$G$的一个单射边染色是指图$G$的一个边染色, 使得距离为$2$的两条边或者在同一个三角形中的两条边染不同的颜色. 图$G$的单射边色数是指图$G$的任意单射边染色所需要的最少颜色数. 关于单射边色数有一个猜想: 任意一个子立方图的单射边色数都不超过$6$. 在本文中, 我们证明了这个猜想对子立方无爪图是成立的, 并且给出图例说明上界$6$是紧的. 同时, 我们的证明隐含了求解这类图不超过$6$种颜色的单射边染色方案的一个线性时间算法.     

Hypohamiltonian Planar Cubic Graphs with Girth 5

A graph is called hypohamiltonian if it is not hamiltonian but becomes hamiltonian if any vertex is removed. Many hypohamiltonian planar cubic graphs have been found, starting with constructions of Thomassen in 1981. However, all the examples found until now had 4‐cycles. In this note we present the first examples of hypohamiltonian planar cubic graphs with cyclic connectivity 5, and thus girth 5. We show by computer search that the smallest members of this class are three graphs with 76 vertices.     

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ( monochromatic components in what follows) have order at most . Ban and Linial Conjectured that every bridgeless cubic graph admits a -bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph with has a -edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (ie, a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we provide evidence of a strong relation of the conjectures of Ban-Linial and Wormald with Ando's Conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above-mentioned conjectures. Moreover, we prove Ban-Linial's Conjecture for cubic-cycle permutation graphs. As a by-product of studying -edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.     

第二小阶数的双本原半对称图

如果一个正则图是边传递但不是点传递的,那么我们称它是半对称的.每一个半对称图X必定是两部分点数相等的二部图,并且它的自同构群Aut(X)在每一部分上是传递的.如果一个半对称图的自同构群在每一部分上作用是本原的,那么我们称它是双本原的.本文决定了第二小阶数的双本原半对称图.     

Bounds on the clique-transversal number of regular graphs

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted Tc(G),is the minimum cardinality of a clique- transversal set in G.In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound.Also,we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.     

Normality of Tetravalent Cayley Graphs of Odd Prime-cube Order and Its Application

Let p be an odd prime. In this paper we prove that all tetravalent connected Cayley graphs of order p^3 are normal. As an application, a classification of tetravalent symmetric graphs of odd prime-cube order is given.     

On Compatible Normal Odd Partitions in Cubic Graphs

A normal odd partition of the edges of a cubic graph is a partition into trails of odd length (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition and internal in some trail. For each vertex v, we can distinguish the edge for which this vertex is pending. Three normal odd partitions are compatible whenever these distinguished edges are distinct for each vertex. We examine this notion and show that a cubic 3‐edge‐colorable graph can always be provided with three compatible normal odd partitions. The Petersen graph has this property and we can construct other cubic graphs with chromatic index four with the same property. Finally, we propose a new conjecture which, if true, would imply the well‐known Fan and Raspaud Conjecture.     

The graphical complexity of direct products of permutation groups

In this article, we improve known results, and, with one exceptional case, prove that when k≥3, the direct product of the automorphism groups of graphs whose edges are colored using k colors, is itself the automorphism group of a graph whose edges are colored using k colors. We have handled the case k = 2 in an earlier article. We prove similar results for directed edge‐colored graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:303‐318, 2011     

On the Toughness of Cycle Permutation Graphs

Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].     

一类半对称图的构造

称一个有限简单无向图X是半对称图,如果图X是正则的且边传递但非点传递.主要利用仿射几何构造了一类2p~n阶连通p~3。度的半对称图的无限族,其中p≥n≥8.     

一类用仿射几何构造的半对称图

图X是一个有限简单无向图,如果图X是正则的且边传递但非点传递,则称X是半对称图.主要利用仿射几何构造了一类2p~n阶连通p~4度的半对称图的无限族,其中p≥n≥11.