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Abstract: A labeling of the vertices of a graph G, OE : V (G) ! f1; : : : ; rg, is said to be r-distinguishing provided no automorphism of the graph preserves all of the vertex labels. The distinguishing number of a graph G, denoted by D(G), is the minimum r such that G has an r-distinguishing labeling. The distinguishing number of the complete graph on t vertices is t. In contrast, we prove (i) given any group \Gamma, there is a graph G such that Aut(G) = \Gamma and D(G) = 2; (ii) D(G) =... (Update)
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.... for which G is d distinguishable is dubbed the distinguishing number of G, denoted #(G) An instantiation of this machinery, mentioned in [1], is the problem of coloring keys on a (circular) key chain so that one can uniquely identify each key. In this case, one is interested...
.... We will say that the graph G realizes if Aut(G) We de ne the distinguishing set of a group by D( fD(G)j G realizes g See [1, 2, 4, 5, 6, 10] for related results. The purpose of this note is to introduce the conjecture below. 2. A conjecture on tournaments Mike Saks...
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BibTeX entry: (Update)
Michael O. Albertson and Karen L. Collins. Symmetry breaking in graphs. Electronic Journal of Combinatorics, 3, 1996. R18. http://citeseer.ist.psu.edu/albertson96symmetry.html More
@misc{ albertson96symmetry,
author = "M. Albertson and K. Collins",
title = "Symmetry breaking in graphs",
text = "Michael O. Albertson and Karen L. Collins. Symmetry breaking in graphs.
Electronic Journal of Combinatorics, 3, 1996. R18.",
year = "1996",
url = "citeseer.ist.psu.edu/albertson96symmetry.html" }
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