| Title:
|
Edge domination in graphs of cubes (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
875-879 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The signed edge domination number and the signed total edge domination number of a graph are considered; they are variants of the domination number and the total domination number. Some upper bounds for them are found in the case of the $n$-dimensional cube $Q_n$. (English) |
| Keyword:
|
signed edge domination number |
| Keyword:
|
signed total edge domination number |
| Keyword:
|
graph of the cube of dimension $n$ |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1009.05102 |
| idMR:
|
MR1940066 |
| . |
| Date available:
|
2009-09-24T10:57:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127771 |
| . |
| Reference:
|
[1] J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater: Signed domination in graphs.In: Graph Theory, Combinatorics and Applications, Y. Alavi, A. J. Schwenk (eds.) vol. 1, Proc. 7th Internat. Conf. Combinatorics, Graph Theory, Applications, John Wiley & Sons, Inc., 1995, pp. 311–322. MR 1405819 |
| Reference:
|
[2] T. Dvořák, I. Havel, J.-M. Laborde and P. Liebl: Generalized hypercubes and graph embedding with dilation.Rostocker Mathematisches Kolloquium 39 (1990), 13–20. MR 1090602 |
| Reference:
|
[3] R. Forcade: Smallest maximal matchings in the graph of the $n$-dimensional cube.J. Combin. Theory Ser. B 14 (1973), 153–156. MR 0321804 |
| Reference:
|
[4] I. Havel and M. Křivánek: On maximal matchings in $Q_6$ and a conjecture of R. Forcade.Comment Math. Univ. Carolin. 23 (1982), 123–136. MR 0653356 |
| Reference:
|
[5] T. W. Haynes, S. T. Hedetniemi and P. J. Slater: Fundamentals of Domination in Graphs.Marcel Dekker, Inc., New York-Basel-Hong Kong, 1998. MR 1605684 |
| Reference:
|
[6] C. Payan: On the chromatic number of cube-like graphs.Discrete Math. 103 (1992), 272–277. Zbl 0772.05043, MR 1171780 |
| Reference:
|
[7] B. Xu: On signed edge domination numbers of graphs.Discrete Math. 239 (2001), 179–189. Zbl 0979.05081, MR 1850997, 10.1016/S0012-365X(01)00044-9 |
| Reference:
|
[8] B. Zelinka: On signed edge domination numbers of trees.Math. Bohem. 127 (2002), 49–55. Zbl 0995.05112, MR 1895246 |
| . |
