一类随机图的演化(英文)  

The Evolution about a Kind of Random Graph

作　　者：王汉兴[1] 马驰[2] 

机构地区：[1]上海立信会计学院数理统计系,上海201620 [2]上海大学数学系

出　　处：《运筹学学报》2006年第1期55-60,共6页Operations Research Transactions

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.10471088, 60572126).

摘　　要：定义一随机图过程:如果图Gt-1不是完全图时,图Gt分别以概率p和q加一个点和一条有向边;如果图Gt-1是完全图时,则以概率1加一个点．研究图Gt顶点和边的概率分布以及当顶点数固定时,边数的期望界值估计．Define a kind of random graph process： the graph G~ recursively from Gt-1 by adding a point or a directed line with probability p and q （q = 1 -p）, respectively, if Gt-1 is not complete graph; if Gt-1 is complete graph, we always add a point with probability 1. By using recursions, we investigate the probability distribution of the order and size of Gt, and of the minimum and maximum sizes for a fixed order. Expected values and generating functions are also determined.

关 键 词：运筹学 随机图过程 完全图 矩母函数 期望值 

分 类 号：O157.5[理学—数学] O211.3[理学—基础数学]