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arXiv · 1511.06378

Characterizing graphs of maximum principal ratio

Michael Tait·Josh Tobin
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Abstract

The principal ratio of a connected graph, denoted $γ(G)$, is the ratio of the maximum and minimum entries of its first eigenvector. Cioabă and Gregory conjectured that the graph on $n$ vertices maximizing $γ(G)$ is a kite graph: a complete graph with a pendant path. In this paper we prove their conjecture.

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Michael Tait, Josh Tobin. 2015-11-19. Characterizing graphs of maximum principal ratio. https://arxiv.org/abs/1511.06378

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