Let G be a connected graph. The principal ratio of G is the ratio of the maximum and minimum entries of its Perron eigenvector. In 2007, Cioabă and Gregory conjectured that among all connected graphs on n vertices, the kite graph attains the maximum principal ratio. In 2018, Tait and Tobin confirmed the conjecture for sufficiently large n. In this article, we show the conjecture is true for all $n\ge 5000$.

中文翻译：

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图的最大本金比率

令G为连通图。G的主要比率是其 Perron 特征向量的最大和最小条目的比率。2007 年，Cioabă 和 Gregory 猜想在所有n个顶点上的连通图中，风筝图达到了最大的主比。2018 年，Tait 和 Tobin 证实了足够大的n猜想。在这篇文章中，我们证明这个猜想对所有人都是正确的$n\ge 5000$.