根圖的穩(wěn)定性及其優(yōu)化
發(fā)布時間：2018-10-24 20:40
【摘要】：設災難發(fā)生時,根圖G的邊以概率p獨立幸存,則含根連通子圖的頂點數的期望值EV(G;p)是根圖的可靠性的合適指標.定義了子圖的頂點數的平方期望值E2(G;p)后,則方差D(G;p)=E2(G;p)-[EV(G;p)]~2是根圖穩(wěn)定性的合適指標.推導得到了E2(G;p)的減-縮邊公式,從而得到方差的一個遞歸計算方法.進而研究了一些特殊圖的方差的計算公式.最后,結合期望和方差,討論了根圖的優(yōu)化問題.
[Abstract]:If the edge of the root graph G survives independently by probability p when a disaster occurs, the expected value EV (Gupp) of the vertex number of the root connected subgraph is an appropriate index for the reliability of the root graph. After defining the square expectation value of the vertex number of a subgraph E _ 2 (G _ p), then the variance D (G _ p) = E _ 2 (G _ p)-[EV (Gupp)] ~ 2 is an appropriate index for the stability of the root graph. In this paper, the formula of reducing and shrinking edges of E2 (Gupp) is derived, and a recursive calculation method of variance is obtained. Furthermore, the formulas for calculating the variance of some special graphs are studied. Finally, the optimization problem of root graph is discussed by combining expectation and variance.
【作者單位】： 白城師范學院數學與統(tǒng)計學院;上海立信會計金融學院統(tǒng)計與數學學院;
【基金】：吉林省自然科學項目(20101564) 吉林省教育科學“十二五”規(guī)劃重點自助課題(ZC12069)
【分類號】：O157.5
，
本文編號：2292497
[Abstract]:If the edge of the root graph G survives independently by probability p when a disaster occurs, the expected value EV (Gupp) of the vertex number of the root connected subgraph is an appropriate index for the reliability of the root graph. After defining the square expectation value of the vertex number of a subgraph E _ 2 (G _ p), then the variance D (G _ p) = E _ 2 (G _ p)-[EV (Gupp)] ~ 2 is an appropriate index for the stability of the root graph. In this paper, the formula of reducing and shrinking edges of E2 (Gupp) is derived, and a recursive calculation method of variance is obtained. Furthermore, the formulas for calculating the variance of some special graphs are studied. Finally, the optimization problem of root graph is discussed by combining expectation and variance.
【作者單位】： 白城師范學院數學與統(tǒng)計學院;上海立信會計金融學院統(tǒng)計與數學學院;
【基金】：吉林省自然科學項目(20101564) 吉林省教育科學“十二五”規(guī)劃重點自助課題(ZC12069)
【分類號】：O157.5
，
本文編號：2292497
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