The reliability polynomial of a graph gives the probability that a graph remains operational when all its edges could fail independently with a certain fixed probability. In general, the problem of finding uniformly most reliable graphs inside a family of graphs, that is, one graph whose reliability is at least as large as any other graph inside the family, is very difficult. In this paper, we study this problem in the family of graphs containing a hamiltonian cycle.

中文翻译：

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汉密尔顿图中的网络可靠性

图的可靠性多项式给出了当图的所有边都可以以一定的固定概率独立失效时，图仍然保持可操作性的概率。通常，很难在一个图族中找到统一最可靠的图，即，一个可靠性至少与该族中任何其他图一样大的图。在本文中，我们在包含哈密尔顿循环的图族中研究了这个问题。