Graphs with convex domination number close to their order

Joanna Cyman, Magdalena Lemańska, and Joanna Raczek. "Graphs with convex domination number close to their order." Discussiones Mathematicae Graph Theory 26.2 (2006): 307-316. <http://eudml.org/doc/270504>.

@article{JoannaCyman2006,
abstract = {For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_\{con\}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.},
author = {Joanna Cyman, Magdalena Lemańska, Joanna Raczek},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {convex domination; Cartesian product},
language = {eng},
number = {2},
pages = {307-316},
title = {Graphs with convex domination number close to their order},
url = {http://eudml.org/doc/270504},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Joanna Cyman
AU - Magdalena Lemańska
AU - Joanna Raczek
TI - Graphs with convex domination number close to their order
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 2
SP - 307
EP - 316
AB - For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_{con}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.
LA - eng
KW - convex domination; Cartesian product
UR - http://eudml.org/doc/270504
ER -