| Title:
|
On the domination of triangulated discs (English) |
| Author:
|
Abd Aziz, Noor A'lawiah |
| Author:
|
Jafari Rad, Nader |
| Author:
|
Kamarulhaili, Hailiza |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
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148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
555-560 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac 14(n+2)$. This conjecture is proved in Tokunaga (2020) for $G-C$ being a tree. In this paper we prove the above conjecture for $G-C$ being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs. (English) |
| Keyword:
|
domination |
| Keyword:
|
double domination |
| Keyword:
|
total domination |
| Keyword:
|
double total domination |
| Keyword:
|
planar graph |
| Keyword:
|
triangulated disc |
| MSC:
|
05C69 |
| DOI:
|
10.21136/MB.2022.0122-21 |
| . |
| Date available:
|
2023-11-23T12:38:54Z |
| Last updated:
|
2023-11-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151974 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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