2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107557The distinguishing number of a graph G, denoted D(G), is the minimum number of colors such that there exists a coloring of the vertices of G where no nontrivial graph automorphism is color-preserving. In this paper, we show that the distinguishing number of p-th graph power of the n-dimensional hypercube is 2 whenever 2 < p < n-1. This completes the study of the distinguishing number of hypercube powers. We also compute the distinguishing number of the augmented cube, a variant of the hypercube, answering an open question.10 pages, 1 figure, submitted to Discrete MathematicsCombinatorics05C25 (Primary), 05C15 (Secondary)text