On distinguishing and distinguishing chromatic numbers of hypercubes
Werner Klöckl (2008)
Discussiones Mathematicae Graph Theory
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The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number of G. Extending these concepts to infinite graphs we prove that and , where denotes the hypercube of countable dimension. We also show that , thereby completing the investigation of finite hypercubes with respect to . Our...