Recognizable colorings of cycles and trees
Michael J. Dorfling ; Samantha Dorfling
Discussiones Mathematicae Graph Theory, Tome 32 (2012), p. 81-90 / Harvested from The Polish Digital Mathematics Library
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For a graph G and a vertex-coloring c:V(G) → 1,2, ...,k, the color code of a vertex v is the (k+1)-tuple (a₀,a₁, ...,aₖ), where a₀ = c(v), and for 1 ≤ i ≤ k, ai is the number of neighbors of v colored i. A recognizable coloring is a coloring such that distinct vertices have distinct color codes. The recognition number of a graph is the minimum k for which G has a recognizable k-coloring. In this paper we prove three conjectures of Chartrand et al. in [8] regarding the recognition number of cycles and trees.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:271084 
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Michael J. Dorfling; Samantha Dorfling. Recognizable colorings of cycles and trees. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 81-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1587/

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