| Title:
|
Convex domination in the composition and Cartesian product of graphs (English) |
| Author:
|
Labendia, Mhelmar A. |
| Author:
|
Canoy, Sergio R. Jr. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
1003-1009 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
convex dominating set |
| Keyword:
|
convex domination number |
| Keyword:
|
clique dominating set |
| Keyword:
|
composition |
| Keyword:
|
Cartesian product |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1274.05356 |
| idMR:
|
MR3010253 |
| DOI:
|
10.1007/s10587-012-0060-3 |
| . |
| Date available:
|
2012-11-10T21:37:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143041 |
| . |
| Reference:
|
[1] Buckley, F., Harary, F.: Distance in Graphs.Addison-Wesley, Redwood City (1990). Zbl 0688.05017 |
| Reference:
|
[2] S. R. Canoy, Jr., I. J. L. Garces: Convex sets under some graph operations.Graphs Comb. 18 (2002), 787-793. Zbl 1009.05054, MR 1964797, 10.1007/s003730200065 |
| Reference:
|
[3] Chartrand, G., Zhang, P.: Convex sets in graphs.Congr. Numerantium 136 (1999), 19-32. Zbl 0967.05031, MR 1744171 |
| Reference:
|
[4] Haynes, T. W., Hedetniemi, S. T., Slater, P. J.: Fundamentals of Domination in Graphs.Marcel Dekker, New York (1998). Zbl 0890.05002, MR 1605684 |
| Reference:
|
[5] Haynes, T. W., Hedetniemi, S. T., Slater, P. J.: Domination in Graphs. Advanced Topics.Marcel Dekker, New York (1998). Zbl 0883.00011, MR 1605685 |
| Reference:
|
[6] Lemańska, M.: Weakly convex and convex domination numbers.Opusc. Math. 24 (2004), 181-188. Zbl 1076.05060, MR 2100881 |
| . |
