| 一类随机图的演化 |
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| 引用本文： | 王汉兴,马驰.一类随机图的演化[J].运筹学学报,2006,10(1):55-60. |
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| 作者姓名： | 王汉兴 马驰 |
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| 作者单位： | 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,上海,200444;安徽理工大学数理系,淮南,232001 |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(Grant No.10471088, 60572126). |
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| 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．
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| 关 键 词： | 运筹学 随机图过程 完全图 矩母函数 期望值 |
| 收稿时间： | 2004-10-12 |
| 修稿时间： | 2004年10月12 |
The Evolution about a Kind of Random Graph |
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| Wang Hanxing,Ma Chi.The Evolution about a Kind of Random Graph[J].OR Transactions,2006,10(1):55-60. |
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| Authors: | Wang Hanxing Ma Chi |
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| Institution: | Department of Mathematics and Statistic, Shanghai Lixin University of Commerce, Shanghai 201620, China; Department of Mathematics, Shanghai University, Shanghai 200444, China; Department of Mathematics and Physics, Anhui University of Science and Technology, Huainan 232001, China |
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| Abstract: | Define a kind of random graph process: the graph Gt 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. |
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| Keywords: | Operation research random graph process complete graph generating function expected value |
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