The distinguishing number of the augmented cube and hypercube powers
Copyright policy )The distinguishing number of the augmented cube and hypercube powers
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.
10 pages, 1 figure, submitted to Discrete Mathematics
- University of Minnesota United States
- Princeton University United States
- University of Minnesota System United States
- College of New Jersey United States
augmented cube, Symmetry breaking, symmetry breaking, hypercube, Theoretical Computer Science, Hypercube, Coloring of graphs and hypergraphs, FOS: Mathematics, 05C25 (Primary), 05C15 (Secondary), Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Distinguishing number, Augmented cube, distinguishing number
augmented cube, Symmetry breaking, symmetry breaking, hypercube, Theoretical Computer Science, Hypercube, Coloring of graphs and hypergraphs, FOS: Mathematics, 05C25 (Primary), 05C15 (Secondary), Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Distinguishing number, Augmented cube, distinguishing number
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