Geodesic
Convex domination in the composition and Cartesian product of graphs
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1003-1009
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we characterize the convex dominating sets in the composition and Cartesian product of two connected graphs. The concepts of clique dominating set and clique domination number of a graph are defined. It is shown that the convex domination number of a composition $G[H]$ of two non-complete connected graphs $G$ and $H$ is equal to the clique domination number of $G$. The convex domination number of the Cartesian product of two connected graphs is related to the convex domination numbers of the graphs involved.
In this paper we characterize the convex dominating sets in the composition and Cartesian product of two connected graphs. The concepts of clique dominating set and clique domination number of a graph are defined. It is shown that the convex domination number of a composition $G[H]$ of two non-complete connected graphs $G$ and $H$ is equal to the clique domination number of $G$. The convex domination number of the Cartesian product of two connected graphs is related to the convex domination numbers of the graphs involved.
DOI : 10.1007/s10587-012-0060-3
Classification : 05C69
Keywords: convex dominating set; convex domination number; clique dominating set; composition; Cartesian product 
@article{10_1007_s10587_012_0060_3,
     author = {Labendia, Mhelmar A. and Canoy, Sergio R. Jr.},
     title = {Convex domination in the composition and {Cartesian} product of graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1003--1009},
     year = {2012},
     volume = {62},
     number = {4},
     doi = {10.1007/s10587-012-0060-3},
     mrnumber = {3010253},
     zbl = {1274.05356},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0060-3/}
}
TY  - JOUR
AU  - Labendia, Mhelmar A.
AU  - Canoy, Sergio R. Jr.
TI  - Convex domination in the composition and Cartesian product of graphs
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 1003
EP  - 1009
VL  - 62
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0060-3/
DO  - 10.1007/s10587-012-0060-3
LA  - en
ID  - 10_1007_s10587_012_0060_3
ER  - 
%0 Journal Article
%A Labendia, Mhelmar A.
%A Canoy, Sergio R. Jr.
%T Convex domination in the composition and Cartesian product of graphs
%J Czechoslovak Mathematical Journal
%D 2012
%P 1003-1009
%V 62
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0060-3/
%R 10.1007/s10587-012-0060-3
%G en
%F 10_1007_s10587_012_0060_3
Labendia, Mhelmar A.; Canoy, Sergio R. Jr. Convex domination in the composition and Cartesian product of graphs. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1003-1009. doi: 10.1007/s10587-012-0060-3

[1] Buckley, F., Harary, F.: Distance in Graphs. Addison-Wesley, Redwood City (1990). | Zbl

[2] S. R. Canoy, Jr., I. J. L. Garces: Convex sets under some graph operations. Graphs Comb. 18 (2002), 787-793. | DOI | MR | Zbl

[3] Chartrand, G., Zhang, P.: Convex sets in graphs. Congr. Numerantium 136 (1999), 19-32. | MR | Zbl

[4] Haynes, T. W., Hedetniemi, S. T., Slater, P. J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998). | MR | Zbl

[5] Haynes, T. W., Hedetniemi, S. T., Slater, P. J.: Domination in Graphs. Advanced Topics. Marcel Dekker, New York (1998). | MR | Zbl

[6] Lemańska, M.: Weakly convex and convex domination numbers. Opusc. Math. 24 (2004), 181-188. | MR | Zbl

Cité par Sources :