Characterizing graphs of maximum principal ratio
Combinatorics
2015-11-23 v1
Abstract
The principal ratio of a connected graph, denoted , is the ratio of the maximum and minimum entries of its first eigenvector. Cioab\u{a} and Gregory conjectured that the graph on vertices maximizing is a kite graph: a complete graph with a pendant path. In this paper we prove their conjecture.
Cite
@article{arxiv.1511.06378,
title = {Characterizing graphs of maximum principal ratio},
author = {Michael Tait and Josh Tobin},
journal= {arXiv preprint arXiv:1511.06378},
year = {2015}
}