New Expected Value Expansions of Rooted Graphs  

作　　者：Xiao-qing TANG 

机构地区：[1]School of Mathematics & Information, Shanghai Lixin University of Commerce

出　　处：《Acta Mathematicae Applicatae Sinica》2015年第1期81-88,共8页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No:60872060;11071158);the Science Foundation of Shanghai Education Committee(No:12ZZ193);the Natural Science Foundation of Shanghai city(No:12ZR1421000)

摘　　要：We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.

关 键 词：rooted graph expected value deletion-contraction edge formula mean-variance optimality 

分 类 号：O157.5[理学—数学]