We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Semitotal domination versus domination and total domination in trees.
- Authors
Zhuang, Wei
- Abstract
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.
- Subjects
DOMINATING set; TREES
- Publication
RAIRO: Operations Research (2804-7303), 2024, Vol 58, Issue 2, p1249
- ISSN
2804-7303
- Publication type
Article
- DOI
10.1051/ro/2024037