Distance 2-Domination in Prisms of Graphs

Ferran Hurtado, et al. "Distance 2-Domination in Prisms of Graphs." Discussiones Mathematicae Graph Theory 37.2 (2017): 383-397. <http://eudml.org/doc/287986>.

@article{FerranHurtado2017,
abstract = {A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.},
author = {Ferran Hurtado, Mercè Mora, Eduardo Rivera-Campo, Rita Zuazua},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {distance 2 dominating set; prisms of graphs; universal fixer},
language = {eng},
number = {2},
pages = {383-397},
title = {Distance 2-Domination in Prisms of Graphs},
url = {http://eudml.org/doc/287986},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Ferran Hurtado
AU - Mercè Mora
AU - Eduardo Rivera-Campo
AU - Rita Zuazua
TI - Distance 2-Domination in Prisms of Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 2
SP - 383
EP - 397
AB - A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.
LA - eng
KW - distance 2 dominating set; prisms of graphs; universal fixer
UR - http://eudml.org/doc/287986
ER -