Open Access
Translator Disclaimer
2005 Salem numbers, Pisot numbers, Mahler measure, and graphs
James McKee, Chris Smyth
Experiment. Math. 14(2): 211-229 (2005).


We use graphs to define sets of Salem and Pisot numbers and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers $n$ the smallest known element of the {\small$n$}th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measure of a graph and find all graphs of Mahler measure less than {\small $\frac12(1+\sqrt{5})$}. Finally, we list all small Salem numbers known to be definable using a graph.


Download Citation

James McKee. Chris Smyth. "Salem numbers, Pisot numbers, Mahler measure, and graphs." Experiment. Math. 14 (2) 211 - 229, 2005.


Published: 2005
First available in Project Euclid: 30 September 2005

zbMATH: 1082.11066
MathSciNet: MR2169524

Primary: 05C50 , 11R06

Keywords: graph spectra , Mahler measure , Pisot Numbers , Salem numbers

Rights: Copyright © 2005 A K Peters, Ltd.


Vol.14 • No. 2 • 2005
Back to Top