The distinguishing number of the hypercube

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Abstract

The distinguishing number of a graph G is the minimum number of colors for which there exists an assignment of colors to the vertices of G so that the group of color-preserving automorphisms of G consists only of the identity. It is shown, for the d-dimensional hypercubic graphs Hd, that D(H d)=3 if d ∈ {2,3} and D(Hd)=2 if d≥4. It is also shown that D(Hd2)=4 for d ∈ {2,3} and D(H d2)=2 for d≥4, where Hd2 denotes the square of the d-dimensional hypercube. This solves the distinguishing number for hypercubic graphs and their squares. © 2004 Elsevier B.V. All rights reserved.

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Bogstad, B., & Cowen, L. J. (2004). The distinguishing number of the hypercube. Discrete Mathematics, 283(1–3), 29–35. https://doi.org/10.1016/j.disc.2003.11.018

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