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1.
设H是图G的一个子图.图G中同构于H的点不交的子图构成的集合称为G的一个H-匹配.图G的H-匹配的最大基数称为是G的H-匹配数,记为ν(H,G).本文主要研究ν(H,G)与G的无符号拉普拉斯谱的关系,同时也讨论了ν(H,G)与G的拉普拉斯谱的关系. 相似文献
2.
XU Qingxiang 《数学年刊B辑(英文版)》2000,21(3):367-374
61. IntroductionLet G be a discrete (not necessarily abelian) group. For any subset G of G, we saythat (G, G ) is a quasi-partial ordered group if e 6 G , G ' G G G and G = G ' G ',where e is the unit of G and G ' = {g--' I g e G }; further, (G, G ) is referred to as aquasi-ordered group if G = G u G '. Note that when G7 = G n G ' = {e}, a quasi-partial ordered group (resp. quasi-ordered group) (G, G ) is known as a pajrtially ordered(resp. ordered) group.Let { 6, I g e G } b… 相似文献
3.
一个有限p-群G称为一个LA-群,如果当G是非循环的且|G|>p~2时有|G|/|Aut(G)|,本文证明了一个含有p~(n-2)阶元的p~n阶p-群是一LA-群。 相似文献
4.
1.IntroductionIn[1],Alavietal.gavethefollowingdecompositionconjecture.Conjecture.LetGbeagraphwith("1')edges.ThentheedgesetofGcanbedecomposedintonsetsgeneratinggraphsGI,G2,'IG.suchthatIE(Gi)I=i(fori=1,2,',n)andGiisisomorphictoasubgraphofGi 1fori=1,2,'.)n--1.AgraphGthatcanbedecomposedasdescribedinConjecturewillbesaidtohaveanAscendingSubgraphDecomposition(AlsoabbreviatedasASD).ThesubgraphsGIIG2,',G.aresaidtobemembersofsuchadecomposition.Furthermore,ifeachGiisastar(matching,pat… 相似文献
5.
有限ATI-群的类保持Coleman自同构 总被引:3,自引:3,他引:0
设G是一个有限群,对G的任意阿贝尔子群A及任意g∈G,若A∩A~g=1或A,则称G为一个ATI-群.本文证明了,对任意p∈τ(G),如果ATI-群G的一个p-方幂阶类保持自同构在G的任意Sylow子群上的限制等于G的某个内自同构的限制,则它必定是一个内自同构.作为该结果的一个直接推论,我们也证明了有限ATI-群G有正规化性质. 相似文献
6.
图的边覆盖染色中的分类问题(英文) 总被引:1,自引:0,他引:1
设 G是一个图 ,其边集是 E( G) ,E( G)的一个子集 S称为 G的一个边覆盖 ,若 G的每一点都是 S中一条边的端点 .G的一个 (正常 )边覆盖染色是对 G的边进行染色 ,使得每一色组都是 G的一个边覆盖 ,使 G有 (正常 )边覆盖染色所需最多颜色数 ,称为 G的边覆盖色数 ,用χ′c( G)表示 .已知的结果是对于任意简单图 G,都有 δ- 1≤ χ′c( G)≤ δ,δ是 G的最小度 .若 χ′c( G) =δ,则称 G是 CI类的 ;否则称为 CII类的 .本文主要研究了平面图及平衡的完全 r分图的分类问题 相似文献
7.
假设G是一个1-可扩图.G的1-因子覆盖是G的某些1-因子的集合M使得∪M∈M M=F(G).1-因子数目最小的1.因子覆盖称为excessive factorization.一个excessive factorization中的1.因子数目称为图G的excessive index,记为x:(G).本文我们基于G的耳朵分解和E(C)的依赖关系给出了X'e(G)的上界.对任意正整数k≥3,我们构造出一个图G使得A(G)=3而X'e(G)=k.进而,我们考虑了乘积图的excessive index. 相似文献
8.
JIANG Lining Department of Mathematics Beijing Institute of Technology Beijing China 《中国科学A辑(英文版)》2005,48(1)
In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γ_G of A_H onto A_G,the C~*-index of γ_G is exactlythe index of H in G. 相似文献
9.
关于l-群的半单结构 总被引:3,自引:0,他引:3
令G是一个l-群,G的一个凸l-子群A叫做多余的,如果对G的任-凸l-子群W,只要A∨W=G,就有W=G.复令R(G)为G的所有多余凸l-子群的集合并生成的凸l-子群.我们证明了R(G)是l-群G的一种报并且是在Amitsur-Kurosh意义下的根.进一步我们得到了有限值l-群的半单结构定理即R(G)=0当且仅当Gl-同构于具有半单性的单l-群的亚直积,同时我们还得到了一系列有意义的推论. 相似文献
10.
On Spectral Integral Variations of Graphs 总被引:4,自引:0,他引:4
Fan Yizheng 《Linear and Multilinear Algebra》2002,50(2):133-142
Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge. 相似文献
11.
设n,m和r是满足r≥2,n≥0,m≥3的整数,且当r是奇数时,假设r≥m-1.称一个图为K1,m-free,如果它不包含以Kt,m为导出的子图.称一个图G为一个(r,n)-临界图,如果在删去G的任意n个点后,剩下G的子图都有一个r-因子,设G是一个Kl,m-free的(n+1)-连通图,且阶为|G|以及r(|G|≥n)是偶数,证明了:如果G的最小度至少是r+n+m-1,阶|G|≥8r5+n,并且对V(G)的任意独立点集{x1,x2}都有|NG(x1)∪NG(x2)|≥(|G|+n)/2,那么G是一个(r,n)-临界图.关于G的最小度和|NG(x1)∪NG(X2)|的下界是紧的。 相似文献
12.
有限群G叫(q)-群,如果G中每个次正规子群均为拟正规子群,群G叫Eq-群,若G中每个子群在G中拟正规或自正规,有限群G叫内Eq-群,如果G本身不是Eq-群,但G的每个真子群是Eq-群,本文确定了Eq-群的结构与内Eq-群的分类. 相似文献
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14.
Fan Yizheng 《Linear and Multilinear Algebra》2013,61(2):133-142
Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge. 相似文献
15.
C_m·S_n的D(2)-点可区别边色数 总被引:1,自引:0,他引:1
对阶数不小于3的连通图G(V,E),设α,β为正整数,令映射f:Ef{1,2,…,α},若u,v∈V(G),1≤d(u,v)≤β,有C(u)≠C(v),则称f为G的一个α-D(β)-点可区别的边染色,简记为α-D(β)-VDPEC,对一个图进行α-D(β)-点可区别的边染色,所需的最少的颜色数称为图G的D(β)-点可区别的边色数,记为χ′β-vd(G),其中d(u,v)表示两个点u,v之间的最短距离.得到了Cm.Sn的D(2)-点可区别边色数. 相似文献
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17.
Wang Yi Fan Yizheng Tan Yingying 《高校应用数学学报(英文版)》2007,22(4):478-484
In this paper,an equivalent condition of a graph G with t(2≤t≤n)distinct Laplacian eigenvalues is established.By applying this condition to t=3,if G is regular(neces- sarily be strongly regular),an equivalent condition of G being Laplacian integral is given.Also for the case of t=3,if G is non-regular,it is found that G has diameter 2 and girth at most 5 if G is not a tree.Graph G is characterized in the case of its being triangle-free,bipartite and pentagon-free.In both cases,G is Laplacian integral. 相似文献
18.
The action of an affine algebraic group G on an algebraic variety V can be
differentiated to a representation of the Lie algebra L(G) of G by derivations on the sheaf
of regular functions on V . Conversely, if one has a finite-dimensional Lie algebra L and a
homomorphism ρ : L → DerK(K[U]) for an affine algebraic variety U, one may wonder whether it comes from an algebraic group action on U or on a variety
V containing U as an open subset. In this paper, we prove two results on this integration problem. First, if L acts faithfully
and locally finitely on K[U], then it can be embedded in L(G), for some affine algebraic group G acting on U, in such a way
that the representation of L(G) corresponding to that action restricts to ρ on L. In the second theorem, we assume from the
start that L = L(G) for some connected affine algebraic group G and show that some technical but necessary conditions on ρ
allow us to integrate ρ to an action of G on an algebraic variety V containing U as an open dense subset. In the interesting
cases where L is nilpotent or semisimple, there is a natural choice for G, and our technical conditions take a more appealing
form. 相似文献
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20.
群G的一个L-模糊正规子群A的陪集做成的群G/A与群G的一个商群是自然同构的。如果f:G→G’是群的满同态,则G’的L-模糊正规子群做成的群与G的在f的核上取定值的L-模糊正规子群做成的群之间存在一个保序的双射。 相似文献