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 between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1322,
author = {Joanna Cyman and Magdalena Lema\'nska and Joanna Raczek},
title = {Graphs with convex domination number close to their order},
journal = {Discussiones Mathematicae Graph Theory},
volume = {26},
year = {2006},
pages = {307-316},
zbl = {1140.05302},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1322}
}
Joanna Cyman; Magdalena Lemańska; Joanna Raczek. Graphs with convex domination number close to their order. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 307-316. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1322/
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