The distinguishing number of the augmented cube and hypercube powers

Details The distinguishing number of the augmented cube and hypercube powers The distinguishing number of the augmented cube and hypercube powers

2006-01-14

arxiv.org/abs/math/0601361v1

Mathematics

Combinatorics

10 pages, 1 figure, submitted to Discrete Mathematics

Scientific paper

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.

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