α-Labelings of a Class of Generalized Petersen Graphs

Anna Benini, and Anita Pasotti. "α-Labelings of a Class of Generalized Petersen Graphs." Discussiones Mathematicae Graph Theory 35.1 (2015): 43-53. <http://eudml.org/doc/271220>.

@article{AnnaBenini2015,
abstract = {An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → \{0, 1, 2, . . . , e\} such that \{|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)\} = \{1, 2, . . . , e\} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of PSn,3.},
author = {Anna Benini, Anita Pasotti},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {generalized Petersen graph; -labeling; graph decomposit; -labeling},
language = {eng},
number = {1},
pages = {43-53},
title = {α-Labelings of a Class of Generalized Petersen Graphs},
url = {http://eudml.org/doc/271220},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Anna Benini
AU - Anita Pasotti
TI - α-Labelings of a Class of Generalized Petersen Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 43
EP - 53
AB - An α-labeling of a bipartite graph Γ of size e is an injective function f : V (Γ) → {0, 1, 2, . . . , e} such that {|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . . , e} and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph PSn,3 admits an α-labeling for any integer n ≥ 1 confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of PSn,3.
LA - eng
KW - generalized Petersen graph; -labeling; graph decomposit; -labeling
UR - http://eudml.org/doc/271220
ER -