一致最可靠完全多部图(英文)On Uniformly Most Reliable Complete Multi-Partite Graphs
于志华,黄晓晖,梁晓东
摘要(Abstract)：
对于一个连通图G,假设边是可靠的而点以p的概率相互独立地发生故障.图G不连通的概率是一个多项式P(G,p).记作Ω (n,m)是有n个点,m条边的连通图的集合.如果对于任意的图H∈Ω (n,m)和任意实数p∈[0,1],P(G,p)≤P(H,p)成立,则称G是Ω (n,m)中的一致最可靠图.本文证明了完全k部图K(b,(b+1)k-3,(b+2)2)是它所在的类中的一致最可靠图.另外,还证明了对任意的h≥2,K(bh,(b+1)k-h-1,(b+2)1)不是其所属类中的一致最可靠图.
关键词(KeyWords)： 网络可靠性;点故障;完全多部图;一致最可靠图
基金项目(Foundation): supported by NSFC(10971255);; the Key Project of Chinese Ministry of Education(208161);; Programfor New Century Excellent Talents in University
作者(Author): 于志华,黄晓晖,梁晓东
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