2021/06/21 by Lele Liu, Liu, Lele, Changxiang He +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2106.10967
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, Cioab\v a 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 sufficientlty large n. In this article, we show the conjecture is true for all n≥ 5000.