# Graphs with convex domination number close to their order

Joanna Cyman; Magdalena Lemańska; Joanna Raczek

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 2, page 307-316
- ISSN: 2083-5892

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topJoanna 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 -

## References

top- [1] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, Inc., 1998). Zbl0890.05002
- [2] Sergio R. Canoy Jr and I.J.L. Garces, Convex sets under some graphs operations, Graphs and Combinatorics 18 (2002) 787-793, doi: 10.1007/s003730200065. Zbl1009.05054

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