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1.
奇阶完备残差图   总被引:2,自引:0,他引:2  
本文讨论奇阶完备残差图,证明了对于任意奇数n,不存在奇阶Kn-残差图.对任意奇数t≥3和n=2t,2t -2,2t-4构造了一类具有奇阶2n+t的Kn-残差图.我们证明了当n≡0(mod4)时,Kn-残差图的最小奇阶为5n/2+1;当n≡2(mod4)时,Kn-残差图的最小奇阶为5n/2,并且证明了相应的最小奇阶Kn-残差图的唯一性.  相似文献   

2.
设G是一个简单无向图,s 3是一个正整数.文章中,若K1,s-匹配数为m(G)的n阶连通图G满足n(s+1)m(G),则G的第m(G)大L-特征值μm(G)s+1,然后证明了类似结论对于Q-谱也成立.最后给出了几个判断图的哈密顿性的Q-特征值条件.  相似文献   

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图的最小Q-特征值是图的二部性的一个度量,具有重要的研究意义.本文研究了移接图G的某些二部分支时最小Q-特征值k(G)的变化规律,推广了文献[Linear Algebra Appl.,2012,436(7):2084-2092]中关于κ(G)的扰动定理.作为应用,本文研究了交错定理的等号成立条件,构造了一个非二部连通图类,并对这图类中每个图G构造一个边子集ε,使得对ε的任意子集S都有κ(G)=κ(G-S).  相似文献   

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对于一个连通图而言,它的最小Q-特征值为零当且仅当它是二部图.图的最小Q-特征值常被用来衡量一个图的非二部程度,因而受到研究者的广泛关注.文中研究了图中存在长路的最小Q-特征值条件,分别确定了最小Q-特征值最小的不含路Pt的非二部单圈图和非二部连通图.  相似文献   

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图的无符号拉普拉斯矩阵是图的邻接矩阵和度对角矩阵的和,其特征值记为q1≥q2≥…≥qn.设C(n,m)是由n个顶点m条边的连通图构成的集合,这里1≤n-1≤m≤(n2).如果对于任意的G∈C(n,m)都有q1(G*)≥q1(G)成立,图G*∈C(n,m)叫做最大图.这篇文章证明了对任意给定的正整数a=m-n+1,如果n...  相似文献   

6.
LD和LD^*设计的存在性   总被引:2,自引:0,他引:2  
设X为n元集,称n~2行s列的表A=(αij)为约束数是s的n阶正交表(记为OA(n,s)),若对任意j,k,1≤j1)  相似文献   

7.
图的最小特征值定义为图的邻接矩阵的最小特征值,它是刻画图的结构性质的重要参数.在给定阶数且补图为具有悬挂点的连通图的图类中,刻画了最小特征值达极小的唯一图,并给出了这类图最小特征值的下界.  相似文献   

8.
李建湘 《经济数学》2002,19(3):19-23
设G是一个n阶图.设1≤a<b是整数.设H1和H2是G的任意两个边不交子图,它们分别具有m1和m5条边,以及δ(G)表示最小度.证明了若δ(G)≥a+m 2,n≥2(d+b-m2)(a+b-m1-1)/(b-m1),a≤b-(m1+m2),并且|NG(x)UNG(y)|≥an/(d+b-m1)+2m2对任意两个不相邻的顶点x和y成立,那么G有[a,b]-因子F使得F含有H1的边并不含H3的边.  相似文献   

9.
图的最小特征值定义为图的邻接矩阵的最小特征值,是刻画图结构性质的一个重要代数参数. 在所有给定阶数的补图为2-点或2-边连通的图中, 刻画了最小特征值达到极小的唯一图, 并给出了这类图最小特征值的下界.  相似文献   

10.
链状正则图的平均距离   总被引:1,自引:0,他引:1  
本文构造了一类链状正则图G_k∶δ,求出了它们的平均距离D(G_k.δ),并得到关系式上式等号成立当且仅当δ=4f且k=0.这个估计式指出了施容华猜想[1]D(G)≤n/(δ 1)不成立. 文中进一步证明了这一类链状正则图有最大的直径,所以可以作出猜想: 若G是n阶连通图,则D(G)<(n 1)/(δ 1),其中δ是图G的最小度。  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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