Salem numbers defined by Coxeter transformation

Lakatos, Piroska (2010) Salem numbers defined by Coxeter transformation. LINEAR ALGEBRA AND ITS APPLICATIONS, 432 (1). pp. 144-154. ISSN 0024-3795

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Abstract

A real algebraic integer alfa > 1 is called a Salem number if all its remaining conjugates have modulus at most 1 with at least one having modulus exactly 1. It is known ([12], [10], [5]) that the spectral radii of Coxeter transformation defined by stars, which are neither of Dynkin nor of extended Dynkin type, are Salem numbers. We prove that the spectral radii of the Coxeter transformation of generalized stars are also Salem numbers. A generalized star is a connected graph without multiple edges and loops that has exactly one vertex of degree at least 3:

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