关于交换群上的Cayley有向图的正规性

Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规,我们定出了交换群上的小度数的非正规的Cayley有向图, 并给出了一个猜想．应用这个结果,给出了pn(n≤2)个点上的度数不超过3的有向对称图的分类,这里p是一个奇素数．     

对称群上的一类Cayley图的边传递性和Hamilton性

Let Sn be the symmetric group,g+I=(123i),g-I=(1i32) and M+n={g+I:4≤I≤n},then M+n is a minimal generating set of Sn,where n≥5.It is proved that Cayley graph Cay(Sn,M+n∪M-n) is Hamiltonian and edge symmetric.     

REFINED CONNECTIVITY PROPERTIES OF ABELIAN CAYLEY GRAPHS

1.IntroductionAgraphG=(V,E)meansafinitegraphwithoutloopsandmultipleedgeswithvertexsetVandedgesetE,theclassicaledgeconnectivityA(G)ofGistheminimumsizeofasetUofedgessuchthatG--Uisdisconnected,andsuchasetUiscalledaoutsetofG.Notethatintheabovedefinition,absolutelynoconditionsorrestrictionsareimposedeitheronthecomponelltsofG--UoronthesetU.ThusitwouldseemnaturaltogeneralizetheconceptofedgeconnectivitybyintroducingsomeconditionsorrestrictionsonthecomponentsofG--Uand/orthesetU.Asageneralizatio…     

THE NORMALITY OF CAYLEY GRAPHS OF SIMPLE GROUP A5 WITH SMALL VALENCIES

Let G be a finite group and S a subset of G not containing the identity element 1. We define the Cayley (di)graph X = Cay(G, S) of G with respect to S by V(X) = G,E(X) = {(g, sg) [ g ∈ G, s ∈ S}. A Cayley (di)graph X = Cay(G, S) is called normal if GR A = Aut(X). In this paper we prove that if S = {a, b, c} is a 3-generating subset of G = A5 not containing the identity 1, then X = Cay(G, S) is a normal Cayley digraph.     

HAMILTONIAN DECOMPOSITION OF CAYLEY GRAPHS OF ORDERS p~2 AND pq

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, …     

ON ABELIAN AUTOMORPHISM GROUPS OF SURFACES OF GENERAL TYPE

1.IntroductionItiswell-knownthatforacomplexcurveofgenusg22,itstotalautomorphismgroup(resp.abelianautomorphismgroup)isoforderS84(g-l)=42degKC(resp.S4g 4),whereKCisthecanonicaldivisorofC(cL[3,4]).Itisanintriguingproblemtogeneralisetheseboundstohigherdimensions.Severalauthorshavestudiedthisproblem(see[5,6]fordetails).Recently,Xiaohasgeneralisedtheseresultstosurfacesofgeneraltype,ingoodanalogywiththecaseofcurves.HehasprovedthatforacomplexminimalsmoothprojectivesurfaceSofgeneraltype,itstota1au…     

对称群上Cayley图的DNA计算

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.     

FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

ＦＩＮＩＴＥＧＲＯＵＰＳＷＨＯＳＥＡＵＴＯＭＯＲＰＨＩＳＭＧＲＯＵＰＨＡＳＯＲＤＥＲＣＵＢＥＦＲＥＥＬＩＳＨＩＲＯＮＧＡｂｓｔｒａｃｔＬｅｔＧｄｅｎｏｔｅａｆｉｎｉｔｅｇｒｏｕｐ．Ｉｔｉｓｓｈｏｗｎｔｈａｔｉｆ｜Ａｕｔ（Ｇ）｜ｉｓｃｕｂｅｆｒｅ...     

凯莱-海森堡群上的格林函数

本文研究凯莱-海森保群上的格林函数.利用凯莱-海森堡群上热核的解析表达式,导出了一阶凯莱-海森堡群上的格林函数的有理分式表示的公式.     

Normal and non-normal Cayley graphs for symmetric groups

A Cayley graph is said to be an NNN-graph if its automorphism group contains two isomorphic regular subgroups where one is normal and the other is non-normal. In this paper, we show that there exist NNN-graphs among the Cayley graphs for symmetric groups $S_n$ if and only if $n?5$.     

ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS

Let G be a finite group and OutCol(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime.In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems.     

一类新的交错群Cayley网络

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。     

Isomorphic Cayley graphs on nonisomorphic groups

The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended. © 1999 John Wiley & Sons, Inc. J Graph Theory 3: 345–362, 1999     

分裂扩张的稳定自同构群

本文给出有限群的分裂的Ａｂｅｌ扩张的稳定自同构群的计算．作为应用,给出了循环群的半直积的自同构群的结构,它包括了若干已知结果,如文［１］的全部结果,并解决了［１］提出的问题．     

关于一类自同构群

本文给出了所有Ｐ＾３阶（ｐ为素数）群的自同构群的结构。     

论连通图的可重构性

本文我们利用带权核子图的可重构性证明了连通图是可重构的,从而证明了重构猜想为真.     

ON MAXIMAL MATCHINGS OF CONNECTED GRAPHS

Let I with |I| = k be a matching of a graph G (briefly, I is called a k-matching). If I is not a proper subset of any other matching of G, then I is a maximal k-matching and m(gk, G) is used to denote the number of maximal k-matchings of G. Let gk be a k-matching of G, if there exists a subset {e1, e2,…, ei} of E(G) \ gk, i (?)1, such that (1) for any j ∈ {1, 2,…,i}, gk + {ej} is a (k + l)-matching of G; (2) for any f ∈ E(G) \ (gk ∪ {e1,e2,…,ei}), gk + {f} is not a matching of G; then gk, is called an i wings k-matching of G and mi(gk,G) is used to denote the number of i wings k-matchings of G. In this paper, it is proved that both mi(gk,G) and m(gk,G) are edge reconstructible for every connected graph G, and as a corollary, it is shown that the matching polynomial is edge reconstructible.     

An infinite family of cubic nonnormal Cayley graphs on nonabelian simple groups

We construct a connected cubic nonnormal Cayley graph on ${\mathrm{A}}_{2^m?1}$ for each integer $m?4$ and determine its full automorphism group. This is the first infinite family of connected cubic nonnormal Cayley graphs on nonabelian simple groups.