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1.
本文研究了Abel群上 Cayley图的Hamilton圈分解的问题.利用"字"和H方操作法,获得了Abel群上4度Cayley图的Hamilton圈分解方案和理论证明.  相似文献   

2.
一、引言图的Hamilton分解问题是图论中的一个引人注目的问题。称一个2k-正则的连通图Γ可以Hamilton分解,是指Γ可以分解为k个Hamilton圈。Alspach在[1]中给出了如下猜测:是否每个2k度连通Cayley图都可以Hamilton分解?文[4]对此问题给出了部分回答,即任意一个4度交换群上连通Cayley图可以分解为2个Hamilton  相似文献   

3.
有一类图称为Cayley图或群图.猜想每个Cayley图都是Hamilton图.求Cayley图和有向Cayley图中的Hamilton圈和路自然产生在计算科学里.这篇文章研究了对称群上Cayley图的DNA计算和给出了求它的Hamilton圈的DNA算法.  相似文献   

4.
主要给出几类非交换群对Alspach猜想(当Cay(G,S)的度小于等于4时)成立,进一步对2n和2p2阶群Cayley图的Hamilton圈的分解进行了讨论.  相似文献   

5.
王艳芳 《工科数学》2009,(5):130-134
主要给出几类非交换群对Alspach猜想(当Cay(G,S)的度小于等于4时)成立,进一步对2n和2p2阶群Cayley图的Hamilton圈的分解进行了讨论.  相似文献   

6.
2pq阶Cayley图是Hamilton图   总被引:3,自引:0,他引:3  
梁海江 《数学季刊》1990,5(3):63-67
一、引言对Cayley图的Hamilton性的研究近几年有所突破[1]现最好的结果是[2]的主要定理:若群G上的换位子群C′是p~n(p是素数,n是正整数)阶循环群时,G上的每个Cayley图皆为Hamilton图。1987年D.Marusic还证明了2p~2(p是素数)阶Cayley图为Hamilton图[4]。本文用群的构造理论证明:2pq(p,q是素数)阶Cayley图是Hamilton图。本文中所提到的群G皆指有限群;群的有关术语和记号同于文献[3];图的有关术  相似文献   

7.
群G的Cayley图Cay(G,S)称为是正规的,如果G的右正则表示R(G)在Cay(G,S)的全自同构群中正规.设p为奇素数,相关文献决定了4p阶连通3度Cayley图的正规性.本文给出了上述文献的主要结果的一个新的简短的证明.  相似文献   

8.
半二面体群的小度数Cayley图   总被引:1,自引:0,他引:1  
群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图.  相似文献   

9.
Cayley图的Hamilton性的若干问题   总被引:3,自引:0,他引:3  
综述近二十年来,研究Cayley图的Hamilton圈的若干新成果,并提出一些未解决问题。  相似文献   

10.
G的Cayley图Cay(G, S)称为是正规的, 如果G的右正则表示R(G)在Cay(G, S)的全自同构群中正规. 给出了非正规 Cayley图的两个充分条件. 应用该结果, 构造了5个连通非正规Cayley图的无限类, 并决定了A5的所有连通5度非正规 Cayley图,从而推广了徐明曜和徐尚进关于A5的连通3、4度Cayley图正规性结果. 此外, 决定了A5的所有连通5度非CI Cayley图.  相似文献   

11.
In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Γ is nHC‐extendable if it contains a path of length n and if every such path is contained in some Hamilton cycle of Γ. Similarly, Γ is weakly nHP‐extendable if it contains a path of length n and if every such path is contained in some Hamilton path of Γ. Moreover, Γ is strongly nHP‐extendable if it contains a path of length n and if for every such path P there is a Hamilton path of Γ starting with P. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2‐HC‐extendable and a complete classification of 3‐HC‐extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4‐HP‐extendable. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory  相似文献   

12.
路在平  徐明曜 《数学进展》2004,33(1):115-120
图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族.  相似文献   

13.
We study connectivity, Hamilton path and Hamilton cycle decomposition, 4-edge and 3-vertex coloring for geometric graphs arising from pseudoline (affine or projective) and pseudocircle (spherical) arrangements. While arrangements as geometric objects are well studied in discrete and computational geometry, their graph theoretical properties seem to have received little attention so far. In this paper we show that they provide well-structured examples of families of planar and projective-planar graphs with very interesting properties. Most prominently, spherical arrangements admit decompositions into two Hamilton cycles; this is a new addition to the relatively few families of 4-regular graphs that are known to have Hamiltonian decompositions. Other classes of arrangements have interesting properties as well: 4-connectivity, 3-vertex coloring or Hamilton paths and cycles. We show a number of negative results as well: there are projective arrangements which cannot be 3-vertex colored. A number of conjectures and open questions accompany our results.  相似文献   

14.
1. IntroductionLet G be a finite group and S a subset of G such that S--1 ~ S, and 1 f S. The Cayleygraph Cay (G, S) is defined as the simple graph with V ~ G, and E = {glgZ I g,'g, or g,'g,6 S, gi, gi E G}. Cay (G, S) is vertex-transitive, and it is connected if and only if (S) = G,i.e. S is a generating set of G[1]. If G = Zn, then Cay (Zn, S) is called a circulant graph. Ithas been proved that any connected Cayley graph on a finite abelian group is hamiltonianl2].Furthermore, …  相似文献   

15.
A Cayley graph Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G, S). In this paper, two sufficient conditions for non-normal Cayley graphs are given and by using the conditions, five infinite families of connected non-normal Cayley graphs are constructed. As an application, all connected non-normal Cayley graphs of valency 5 on A5 are determined, which generalizes a result about the normality of Cayley graphs of valency 3 or 4 on A5 determined by Xu and Xu. Further, we classify all non-CI Cayley graphs of valency 5 on A5, while Xu et al. have proved that As is a 4-CI group.  相似文献   

16.
An LR structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR structures were introduced in Potočnik and Wilson (2014) as a tool to study tetravalent semisymmetric graphs of girth 4. In this paper, we consider algebraic methods of constructing LR structures, using number theory, Cayley graphs, affine groups, abelian groups and fields.  相似文献   

17.
本文利用交错群的Cayley图构作了一类互连网络,进而讨论了它的直径,容错度,容错直径和Hamilton连通性,这些性质表明它优于利用交错群构作的网络AGn,且相似于著名的星形网络。  相似文献   

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