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2017 Volume 42 Issue 4
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WANG Bing-jie,TANG Xiao-qing. On Stability of Rooted Graph and Its Optimality[J]. Journal of Southwest China Normal University(Natural Science Edition), 2017, 42(4). doi: 10.13718/j.cnki.xsxb.2017.04.003
Citation: WANG Bing-jie,TANG Xiao-qing. On Stability of Rooted Graph and Its Optimality[J]. Journal of Southwest China Normal University(Natural Science Edition), 2017, 42(4). doi: 10.13718/j.cnki.xsxb.2017.04.003
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On Stability of Rooted Graph and Its Optimality

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  • When G is a rooted graph where each edge may independently succeed with probability p when catastrophic thing happens, we consider the expected number of vertices in the operational component of G containing the root.Then the expected value of edges number EV(G;p) is a proper index of reliability to rooted graph.Later, we give the definition E2(G;p), which is the expect of vertices number square, then variance D(G;p)=E2(G;p)-[EV(G;p)]2.Especially, we get the deletion-contraction edge formula of E2(G;p).So we obtain a recursive computing variance method.And D(G;p) is a proper stability index to the rooted graph.With this formula, we get some variance computational formulas of specific rooted graphs.Finally, we propose expect-variance optimality of rooted graph.
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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On Stability of Rooted Graph and Its Optimality

Abstract: When G is a rooted graph where each edge may independently succeed with probability p when catastrophic thing happens, we consider the expected number of vertices in the operational component of G containing the root.Then the expected value of edges number EV(G;p) is a proper index of reliability to rooted graph.Later, we give the definition E2(G;p), which is the expect of vertices number square, then variance D(G;p)=E2(G;p)-[EV(G;p)]2.Especially, we get the deletion-contraction edge formula of E2(G;p).So we obtain a recursive computing variance method.And D(G;p) is a proper stability index to the rooted graph.With this formula, we get some variance computational formulas of specific rooted graphs.Finally, we propose expect-variance optimality of rooted graph.

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