| Title:
|
On signed majority total domination in graphs (English) |
| Author:
|
Xing, Hua-Ming |
| Author:
|
Sun, Liang |
| Author:
|
Chen, Xue-Gang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
341-348 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We initiate the study of signed majority total domination in graphs. Let $G=(V,E)$ be a simple graph. For any real valued function $f\: V \rightarrow \mathbb{R}$ and ${S\subseteq V}$, let $f(S)=\sum _{v\in S}f(v)$. A signed majority total dominating function is a function $f\: V\rightarrow \lbrace -1,1\rbrace $ such that $f(N(v))\ge 1$ for at least a half of the vertices $v\in V$. The signed majority total domination number of a graph $G$ is $\gamma _{{\mathrm maj}}^{{\,\mathrm t}}(G)=\min \lbrace f(V)\mid f$ is a signed majority total dominating function on $G\rbrace $. We research some properties of the signed majority total domination number of a graph $G$ and obtain a few lower bounds of $\gamma _{{\mathrm maj}}^{{\,\mathrm t}}(G)$. (English) |
| Keyword:
|
signed majority total dominating function |
| Keyword:
|
signed majority total domination number |
| MSC:
|
05C35 |
| idZBL:
|
Zbl 1081.05049 |
| idMR:
|
MR2137141 |
| . |
| Date available:
|
2009-09-24T11:23:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127981 |
| . |
| Reference:
|
[1] B. Zelinka: Signed total domination number of a graph.Czechoslovak Math. J. 51 (2001), 225–229. Zbl 0977.05096, MR 1844306, 10.1023/A:1013782511179 |
| Reference:
|
[2] I. Broere, J. H. Hattingh, M. A. Henning and A. A. McRae: Majority domination in graphs.Discrete Math. 138 (1995), 125–135. MR 1322087, 10.1016/0012-365X(94)00194-N |
| Reference:
|
[3] J. H. Hattingh: Majority domination and its generalizations.Domination in Graphs: Advanced Topics, T. W. Haynes, S. T. Hedetniemi,and P. J. Slater (eds.), Marcel Dekker, New York, 1998. Zbl 0891.05042, MR 1605689 |
| Reference:
|
[4] T. S. Holm: On majority domination in graph.Discrete Math. 239 (2001), 1–12. MR 1850982, 10.1016/S0012-365X(00)00370-8 |
| . |
