用计数平凡割求一致最可靠图
Finding uniformly most reliable graphs by counting trivial cuts
摘要：
有大量的文献集中在网络可靠性评估。在过去的几十年里，可靠性优化也得到了解决。Frank Boesch在1986年提出了一致最可靠图（UMRG）的概念。后来，Boesch \emph{et al.}提出了第一个UMRG，并证明了二部完全图$K_{3,3}$的某些特殊子图以及二部完全图$K_{4,4}$都是UMRG。王证明了第一个猜想是正确的。Wendy Myrvold通过计算测试证实了$K_{4,4}$也是UMRG。然而，迄今为止，在文献中没有数学证明。平凡割是包含固定节点的所有关联边的边集。在这篇文章中，我们描述了一种方法来确定UMRG的基础上界定的平凡削减的数量。作为概念证明，证明了$K_{3,3}$和$K_{4,4}$都是UMRG。
英文摘要：
There is a vast literature focused on network reliability evaluation. In the last decades, reliability optimization has been also addressed. Frank Boesch in 1986 introduced the concept of uniformly most reliable graph (UMRG). Later, Boesch \emph{et al.} presented the first UMRGs and conjectured that some special subdivisions of the bipartite complete graph $K_{3,3}$, as well as the bipartite complete graph $K_{4,4}$, are UMRGs. Wang proved that the first conjecture is true. Wendy Myrvold confirmed that $K_{4,4}$ is also UMRG, by means of computational tests. However, thus far, there is no mathematical proof in the literature. A trivial cut is an edge-set that includes all the incident edges of a fixed node. In this article we describe a methodology to determine UMRGs based on bounding the number of trivial cuts. As a proof-of-concept it is proved that both $K_{3,3}$ and $K_{4,4}$ are UMRGs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
