Geodesic
The canonical coloring graph of trees and cycles
Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 149-157.

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For a graph G and an ordering of the vertices π, the set of canonical k-colorings of G under π is the set of non-isomorphic proper k-colorings of G that are lexicographically least under π. The canonical coloring graph Canπk(G) is the graph with vertex set the canonical colorings of G and two vertices are adjacent if the colorings differ in exactly one place. This is a natural variation of the color graph Ck(G) where all colorings are considered. We show that every graph has a canonical coloring graph which is disconnected; that trees have canonical coloring graphs that are Hamiltonian; and cycles have canonical coloring graphs that are connected.
DOI : 10.26493/1855-3974.168.464
Keywords: Graph Coloring, Canonical coloring 
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Ruth Haas. The canonical coloring graph of  trees and cycles. Ars Mathematica Contemporanea, Tome 5 (2012) no. 1, pp. 149-157. doi : 10.26493/1855-3974.168.464. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.168.464/

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