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{\bf Karen L. Collins and Ann N. Trenk }
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{\bf The Distinguishing Chromatic Number}
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In this paper we define and study the distinguishing chromatic number,
$\chi_D(G)$, of a graph $G$, building on the work of Albertson and
Collins who studied the distinguishing number. We find $\chi_D(G)$
for various families of graphs and characterize those graphs with
$\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic
distingushing number for trees. We prove analogs of Brooks' Theorem
for both the distinguishing number and the distinguishing chromatic
number, and for both trees and connected graphs. We conclude with
some conjectures.
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