The maximum principal ratio of graphs
Lele Liu, Changxiang He · Linear and Multilinear Algebra · 2022
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≥5000.