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Keywords

Irregular graph, eigenvector, principal ratio

Abstract

The principal ratio of a connected graph, denoted γ(G), is the ratio of the maximum and minimum entries of its Perron eigenvector. Cioaba and Gregory (2007) conjectured that the graph on n vertices maximizing γ(G) is a kite graph, that is, a complete graph with a pendant path. In this paper, their conjecture is proved

abs_vol34_pp61-70.pdf (98 kB)
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