The spectral radius of the Galois covering of a finite graph

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Abstract

Let π:Δ→Δ′ be a Galois covering of a finite graph Δ′ defined by the action of a group G. We study the problem of the relation between the spectral radius r(Δ) of Δ and that of Δ′. We show that r(Δ)≤r(Δ′)≤r(Δ)2. We prove that in case the group G is amenable, then r(Δ)=r(Δ′). © 1992.

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de la Peña, J. A., & Takane, M. (1992). The spectral radius of the Galois covering of a finite graph. Linear Algebra and Its Applications, 160(C), 175–188. https://doi.org/10.1016/0024-3795(92)90446-H

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