首页 | 本学科首页   官方微博 | 高级检索  
文章检索
  按 检索   检索词:      
出版年份:   被引次数:   他引次数: 提示:输入*表示无穷大
  收费全文   6篇
  完全免费   1篇
  数学   7篇
  2018年   1篇
  2012年   1篇
  2011年   1篇
  2003年   1篇
  2002年   2篇
  2001年   1篇
排序方式: 共有7条查询结果,搜索用时 78 毫秒
1
1.
Connected Components in Random Graphs with Given Expected Degree Sequences   总被引:1,自引:0,他引:1  
We consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its endpoints. We examine the distribution of the sizes/volumes of the connected components which turns out depending primarily on the average degree d and the second-order average degree d~. Here d~ denotes the weighted average of squares of the expected degrees. For example, we prove that the giant component exists if the expected average degree d is at least 1, and there is no giant component if the expected second-order average degree d~ is at most 1. Examples are given to illustrate that both bounds are best possible.  相似文献
2.
David Vogan gave programmatic conjectures about the Dixmier's map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed[1]. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan's first conjecture for geometric orbit datum:the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan's conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.``  相似文献
3.
Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{mk} (1+ o(1))\sqrt{m_k} where mk is the k-th largest expected degree provided mk is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.  相似文献
4.
We consider the diameter of a random graph G(np) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of random graph G(np) is close to if np → ∞. Moreover if , then the diameter of G(np) is concentrated on two values. In general, if , the diameter is concentrated on at most 21/c0 + 4 values. We also proved that the diameter of G(np) is almost surely equal to the diameter of its giant component if np > 3.6.  相似文献
5.
6.
The Randi? indexR(G) of a graph G is defined as the sum of over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of G when G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G)−D(G). We prove this conjecture completely. In fact, we prove a stronger theorem: If G is a connected graph, then , with equality if and only if G is a path with at least three vertices.  相似文献
7.
在本文中,令$\rho_r=\sqrt[r]{4}$和$\rho_r''=\beta^{-1/r}$, 其中 $\beta=-\frac{1}{6}\cdot(100+12\cdot \sqrt{69})^{\frac{1}{3}}-\frac{2}{3\cdot(100+12\cdot\sqrt{69})^{\frac{1}{3}}}+\frac{4}{3}\approx 0.2451223338$, 们研究了谱半径位于$\rho_{r}$ 和 $\rho''_{r}$之间的连通的$r$-一致超图,并对这样的超图给出了描述.  相似文献
1
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号