| Title:
|
Signed total domination number of a graph (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
225-229 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The signed total domination number of a graph is a certain variant of the domination number. If $v$ is a vertex of a graph $G$, then $N(v)$ is its oper neighbourhood, i.e. the set of all vertices adjacent to $v$ in $G$. A mapping $f: V(G) \rightarrow \lbrace -1, 1\rbrace $, where $V(G)$ is the vertex set of $G$, is called a signed total dominating function (STDF) on $G$, if $\sum _{x \in N(v)} f(x) \ge 1$ for each $v \in V(G)$. The minimum of values $\sum _{x \in V(G)} f(x)$, taken over all STDF’s of $G$, is called the signed total domination number of $G$ and denoted by $\gamma _{\mathrm st}(G)$. A theorem stating lower bounds for $\gamma _{\mathrm st}(G)$ is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on $n$-side prisms. At the end it is proved that $\gamma _{\mathrm st}(G)$ is not bounded from below in general. (English) |
| Keyword:
|
signed total dominating function |
| Keyword:
|
signed total domination number |
| Keyword:
|
regular graph |
| Keyword:
|
circuit |
| Keyword:
|
complete graph |
| Keyword:
|
complete bipartite graph |
| Keyword:
|
Cartesian product of graphs |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 0977.05096 |
| idMR:
|
MR1844306 |
| . |
| Date available:
|
2009-09-24T10:41:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127643 |
| . |
| Reference:
|
[1] J. E.Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater: Signed domination in graphs.Graph Theory, Combinatorics and Application, Proceedings 7th Internat. Conf. Combinatorics, Graph Theory, Applications, vol. 1, Y. Alavi, A. J. Schwenk (eds.), John Willey & Sons, Inc., 1995, pp. 311–322. MR 1405819 |
| Reference:
|
[2] 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 |
| . |
