Convex domination in the composition and Cartesian product of graphs
Mhelmar A. Labendia; Sergio R. Jr. Canoy
Czechoslovak Mathematical Journal (2012)
- Volume: 62, Issue: 4, page 1003-1009
- ISSN: 0011-4642
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topLabendia, Mhelmar A., and Canoy, Sergio R. Jr.. "Convex domination in the composition and Cartesian product of graphs." Czechoslovak Mathematical Journal 62.4 (2012): 1003-1009. <http://eudml.org/doc/246600>.
@article{Labendia2012,
abstract = {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.},
author = {Labendia, Mhelmar A., Canoy, Sergio R. Jr.},
journal = {Czechoslovak Mathematical Journal},
keywords = {convex dominating set; convex domination number; clique dominating set; composition; Cartesian product; convex dominating set; convex domination number; clique dominating set; composition; Cartesian product},
language = {eng},
number = {4},
pages = {1003-1009},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convex domination in the composition and Cartesian product of graphs},
url = {http://eudml.org/doc/246600},
volume = {62},
year = {2012},
}
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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 1003
EP - 1009
AB - 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.
LA - eng
KW - convex dominating set; convex domination number; clique dominating set; composition; Cartesian product; convex dominating set; convex domination number; clique dominating set; composition; Cartesian product
UR - http://eudml.org/doc/246600
ER -
References
top- Buckley, F., Harary, F., Distance in Graphs, Addison-Wesley, Redwood City (1990). (1990) Zbl0688.05017
- S. R. Canoy, Jr., I. J. L. Garces, 10.1007/s003730200065, Graphs Comb. 18 (2002), 787-793. (2002) Zbl1009.05054MR1964797DOI10.1007/s003730200065
- Chartrand, G., Zhang, P., Convex sets in graphs, Congr. Numerantium 136 (1999), 19-32. (1999) Zbl0967.05031MR1744171
- Haynes, T. W., Hedetniemi, S. T., Slater, P. J., Fundamentals of Domination in Graphs, Marcel Dekker, New York (1998). (1998) Zbl0890.05002MR1605684
- Haynes, T. W., Hedetniemi, S. T., Slater, P. J., Domination in Graphs. Advanced Topics, Marcel Dekker, New York (1998). (1998) Zbl0883.00011MR1605685
- Lemańska, M., Weakly convex and convex domination numbers, Opusc. Math. 24 (2004), 181-188. (2004) Zbl1076.05060MR2100881
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