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.
@article{bwmeta1.element.doi-10_7151_dmgt_1946,
author = {Ferran Hurtado and Merc\`e Mora and Eduardo Rivera-Campo and Rita Zuazua},
title = {Distance 2-Domination in Prisms of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {383-397},
zbl = {06705135},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1946}
}
Ferran Hurtado; Mercè Mora; Eduardo Rivera-Campo; Rita Zuazua. Distance 2-Domination in Prisms of Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 383-397. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1946/