2006/01/14 by Melody Chan, Chan, Melody
Computer Science · Materials Science · #05C15 (Secondary) #05C25 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Photochromic and Fluorescence Chemistry
paper · pdf · doi:10.48550/arxiv.math/0601361
openalex publication_date 2006/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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.