Recognizable colorings of cycles and trees

Michael J. Dorfling, and Samantha Dorfling. "Recognizable colorings of cycles and trees." Discussiones Mathematicae Graph Theory 32.1 (2012): 81-90. <http://eudml.org/doc/271084>.

@article{MichaelJ2012,
abstract = {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, $a_i$ 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.},
author = {Michael J. Dorfling, Samantha Dorfling},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {recognizable coloring; recognition number},
language = {eng},
number = {1},
pages = {81-90},
title = {Recognizable colorings of cycles and trees},
url = {http://eudml.org/doc/271084},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Michael J. Dorfling
AU - Samantha Dorfling
TI - Recognizable colorings of cycles and trees
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 1
SP - 81
EP - 90
AB - 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, $a_i$ 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.
LA - eng
KW - recognizable coloring; recognition number
UR - http://eudml.org/doc/271084
ER -