随机图的谱矩(英文)  

Spectral Moment of Random Graphs

作　　者：陈志[1] 范益政[1] 杜文学[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230039

出　　处：《应用数学》2011年第4期851-857,共7页Mathematica Applicata

基　　金：National Natural Science Foundation of China(11071002);Program for New Century Excellent Talents in University,Key Project of Chinese Ministry of Education(210091);Specialized Research Fund for the Doctoral Program of Higher Education(20103401110002);Anhui Provincial Natural Science Foundation(10040606Y33);Project of Educational Department of Anhui Province(KJ2010B136);Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University,Project for Academic Innovation Team of Anhui University(KJTD001B)

摘　　要：简单图G的k阶谱矩定义为G的特征值的k阶幂之和,记为Mk(G).应用概率和代数的方法,对于几乎所有的图G,本文给出Mk(G)的一个精确估计.此外,对于几乎所有的多部图G,本文给出了Mk(G)的上界和下界.The k-th spectral moment for a simple graph G,denoted by Mk（G）,is the sum of k-th power of eigenvalues of G.By probabilistic and algebraic approaches,we formulate an exact estimate to Mk（G） for almost all graphs.Furthermore,we establish a lower and upper bound to Mk（G） for almost all multipartite graphs.

关 键 词：Erds-Rényi随机图 随机多部图 特征值 谱矩 

分 类 号：O157.5[理学—数学]