On Distinguishing and Distinguishing Chromatic Numbers of Hypercubes
نویسنده
چکیده
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 χD(G) of G. Extending these concepts to infinite graphs we prove that D(Qא0) = 2 and χD(Qא0) = 3, where Qא0 denotes the hypercube of countable dimension. We also show that χD(Q4) = 4, thereby completing the investigation of finite hypercubes with respect to χD. Our results extend work on finite graphs by Bogstad and Cowen on the distinguishing number and Choi, Hartke and Kaul on the distinguishing chromatic number.
منابع مشابه
The distinguishing chromatic number of bipartite graphs of girth at least six
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