2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74598We 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 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 (1+sqrt5)/2. Finally, we list all small Salem numbers known to be definable using a graph.28 pages, 7 figuresNumber Theory11R06;05C50text