Geodesic
The distinguishing chromatic number
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1042
Classification : 05C15, 05C25 
@article{10_37236_1042,
     author = {Karen L. Collins and Ann N. Trenk},
     title = {The distinguishing chromatic number},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1042},
     zbl = {1081.05033},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1042/}
}
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Karen L. Collins; Ann N. Trenk. The distinguishing chromatic number. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1042

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