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## Discussiones Mathematicae Graph Theory

2006 | 26 | 2 | 307-316
Tytuł artykułu

### Graphs with convex domination number close to their order

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EN
Abstrakty
EN
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.
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EN
Kategorie tematyczne
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Tom
Numer
Strony
307-316
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-01-21
poprawiono
2005-11-18
Twórcy
autor
• Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland
autor
• Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland
autor
• Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland
Bibliografia
• [1] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, Inc., 1998).
• [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.
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