Double domination critical and stable graphs upon vertex removal

Soufiane Khelifi, and Mustapha Chellali. "Double domination critical and stable graphs upon vertex removal." Discussiones Mathematicae Graph Theory 32.4 (2012): 643-657. <http://eudml.org/doc/271030>.

@article{SoufianeKhelifi2012,
abstract = {In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted $γ_\{×2\}(G)$, is the minimum cardinality among all double dominating sets of G. We consider the effects of vertex removal on the double domination number of a graph. A graph G is $γ_\{×2\}$-vertex critical graph ($γ_\{×2\}$-vertex stable graph, respectively) if the removal of any vertex different from a support vertex decreases (does not change, respectively) $γ_\{×2\}$(G). In this paper we investigate various properties of these graphs. Moreover, we characterize $γ_\{×2\}$-vertex critical trees and $γ_\{×2\}$-vertex stable trees.},
author = {Soufiane Khelifi, Mustapha Chellali},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {double domination; vertex removal critical graphs; vertex removal stable graphs},
language = {eng},
number = {4},
pages = {643-657},
title = {Double domination critical and stable graphs upon vertex removal},
url = {http://eudml.org/doc/271030},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Soufiane Khelifi
AU - Mustapha Chellali
TI - Double domination critical and stable graphs upon vertex removal
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 4
SP - 643
EP - 657
AB - In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted $γ_{×2}(G)$, is the minimum cardinality among all double dominating sets of G. We consider the effects of vertex removal on the double domination number of a graph. A graph G is $γ_{×2}$-vertex critical graph ($γ_{×2}$-vertex stable graph, respectively) if the removal of any vertex different from a support vertex decreases (does not change, respectively) $γ_{×2}$(G). In this paper we investigate various properties of these graphs. Moreover, we characterize $γ_{×2}$-vertex critical trees and $γ_{×2}$-vertex stable trees.
LA - eng
KW - double domination; vertex removal critical graphs; vertex removal stable graphs
UR - http://eudml.org/doc/271030
ER -