| Issue |
RAIRO-Oper. Res.
Volume 58, Number 2, March-April 2024
|
|
|---|---|---|
| Page(s) | 1249 - 1256 | |
| DOI | https://doi.org/10.1051/ro/2024037 | |
| Published online | 27 March 2024 | |
Semitotal domination versus domination and total domination in trees
School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, P.R. China
* Corresponding author: zhuangweixmu@163.com
Received:
4
September
2023
Accepted:
5
February
2024
A set S of vertices in G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating set of G. Clearly, γ(G) ≤ γt2(G) ≤ γt(G). In this paper, for any nontrivial tree T that is not a star, we investigate the ratios γt2(T )/γ(T) and γt(T )/γt2(T), and provide constructive characterizations of trees achieving the upper bounds.
Mathematics Subject Classification: 05C69
Key words: Domination number / total domination number / semitotal domination number
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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