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1.
Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1  相似文献   

2.
历史上的某一天是星期几?未来的某一天是星期几?关于这些问题,有很多计算公式,其中最著名的是蔡勒(Zeller)公式:训。y+[y/4]+[c/4]-2c+[2.6(m+1)]+d-1.  相似文献   

3.
文[1]给出了函数f(x)=Ca^x+D/Aa^x+B对称中心,文[2]又给出了函数g(x)=1g(cx+d/ax+b)的对称中心,这两个函数同时具备中心对称的性质,是孤立的还是有某种联系呢?以它们最特殊的两个函数f(x)=a^x+1/a^x-1,  相似文献   

4.
任宪伟 《数学通讯》2010,(10):16-17
2010年高考湖北卷理科第(9)题为:若直线y=x+b与曲线y=3-√4x-x^2有公共点,则实数b的取值范围是 ( ) (A)[-1,1+2√2]. (B)[-1-2√2,1+2√2]. (C)[1-2√2,3]. (D)[1-√2,3].  相似文献   

5.
2005年巴尔干数学奥林匹克试题的第3题是: 设a,b,C是正数,求证: α^2/b+b^2/c+c^2/α≥α+b+c+4(α-b)^2/α+b+c (1) 文[1]从变量的个数方面给出了一个推广:  相似文献   

6.
厉倩 《数学通讯》2006,(5):15-16
湖北卷(理)22题:已知不等式1/2+1/3+…+1/n〉1/2[log2 n],其中n为大于2的整数,[log2 n]表示不超过log2 n的最大整数,设数列|an|的各项为正,且满足:a1=b(b〉0),an≤nan-1/n+an-1,n=2,3,4…,  相似文献   

7.
文[1]给出了等差数列的一个性质如下: 对于任意公差为d的等差数列{an},且.an≠0.总有: (-1)^0Cn^0/a1+(-1)^1Cn^1/a^2+(-1)^2Cn^2/a3+…+(-1)^iCn^i/ai+1+…^(-1)^nCn^n/an+1=n!d^n/a1·a2…an 文[2]又给出了等比数列的一个类似的性质如下:  相似文献   

8.
文[1]探索证明了函数y=lgcx/d/αax+b(αd≠bc,cα≠0)的图象是中心对称图形,它的对称中心是-d/c+d/α/2,lg(c/α),但过程稍显繁琐,笔者认为用结论:“函数f(x)的图象有对称中心(h,k)的充要条件是对定义域中的任何一个x,均有f(h+x)+f(h-x)=2k.”证明较为简洁明了.证明如下:  相似文献   

9.
文[1]中给出了下列结果: 已知x1,x2,…,xn∈R^+则 x1^2/x2+x2^2/x3+…+xn^2/x1 ≥x1+x2+…+xn+4(x1-x2)^2/x1+x2+…+xn (1)[编者按]  相似文献   

10.
文[1]用放缩法证明了这样一个不等式:已知”为正整数,求证;1^2(1/4)+2^2(1/4)^2+3^2(1/4)^3+……+n^2(1/4)^n〈49/64.  相似文献   

11.
The spectrum of weighted graphs is often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the (signless) Laplacian spectral radius of weighted graphs when some weights of edges are modified; we then determine the weighted tree with the largest Laplacian spectral radius in the set of all weighted trees with a fixed number of pendant vertices and a positive weight set. Furthermore, we also derive the weighted trees with the largest Laplacian spectral radius in the set of all weighted trees with a fixed positive weight set and independence number, matching number or total independence number.  相似文献   

12.
The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we provide structural and behavioral details of graphs with maximum Laplacian spectral radius among all bipartite connected graphs of given order and size. Using these results, we provide a unified approach to determine the graphs with maximum Laplacian spectral radii among all trees, and all bipartite unicyclic, bicyclic, tricyclic and quasi-tree graphs, respectively.  相似文献   

13.
In this paper, we study the largest Laplacian spectral radius of the bipartite graphs with n vertices and k cut edges and the bicyclic bipartite graphs, respectively. Identifying the center of a star K1,k and one vertex of degree n of Km,n, we denote by the resulting graph. We show that the graph (1?k?n-4) is the unique graph with the largest Laplacian spectral radius among the bipartite graphs with n vertices and k cut edges, and (n?7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs.  相似文献   

14.
In this paper, we consider the following problem: of all tricyclic graphs or trees of order n with k pendant vertices (n,k fixed), which achieves the maximal signless Laplacian spectral radius?We determine the graph with the largest signless Laplacian spectral radius among all tricyclic graphs with n vertices and k pendant vertices. Then we show that the maximal signless Laplacian spectral radius among all trees of order n with k pendant vertices is obtained uniquely at Tn,k, where Tn,k is a tree obtained from a star K1,k and k paths of almost equal lengths by joining each pendant vertex to one end-vertex of one path. We also discuss the signless Laplacian spectral radius of Tn,k and give some results.  相似文献   

15.
张建斌  周波 《数学研究》2011,44(2):160-169
图的邻接矩阵的最大特征值称为图的谱半径.对于n≥8,1≤k≤n+23,本文确定了n个顶点和至少有惫个顶点度不少于3的树中具有谱半径最大的树.  相似文献   

16.
关于谱半径达到第二大的赋权树   总被引:1,自引:0,他引:1  
赋权图的谱的研究已经被用来解决很多实际问题,网络设计以及电路设计实际上都依赖于赋权图.本文主要研究的是赋权树的谱半径,从而得到赋权树谱半径达到次大的是双星图Sn-3,1ω*.  相似文献   

17.
Let T be a tree with n vertices and let A(T) be the adjacency matrix of T. Spectral radius of T is the largest eigenvalue of A(T). Wu et al. [Wu, B.F., Yuan, X.Y, and Xiao, E.L. On the spectral radii of trees, Journal of East China Normal University (Natural Science), 3:22-28 (2004)] determined the first seven trees of order n with the smallest spectral radius. In this paper, we extend this ordering by determining the trees with the eighth to the tenth smallest spectral radius among all trees with n vertices.  相似文献   

18.
We establish a useful correspondence between the closed walks in regular graphs and the walks in infinite regular trees, which, after counting the walks of a given length between vertices at a given distance in an infinite regular tree, provides a lower bound on the number of closed walks in regular graphs. This lower bound is then applied to reduce the number of the feasible spectra of the 4-regular bipartite integral graphs by more than a half.Next, we give the details of the exhaustive computer search on all 4-regular bipartite graphs with up to 24 vertices, which yields a total of 47 integral graphs.  相似文献   

19.
A connected graph G =(V, E) is called a quasi-tree graph, if there exists a vertex v_0 ∈ V(G) such that G-v_0 is a tree. Liu and Lu [Linear Algebra Appl. 428(2008) 2708-2714] determined the maximal spectral radius together with the corresponding graph among all quasi-tree graphs on n vertices. In this paper, we extend their result, and determine the second to the fifth largest spectral radii together with the corresponding graphs among all quasi-tree graphs on n vertices.  相似文献   

20.
In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the all unicyclic graphs with n vertices and k pendant vertices is identified. Furthermore, we determine the graphs with the largest Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with n vertices and k pendant vertices, respectively.  相似文献   

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