Computational complexity aspects of super domination
Journal article, Peer reviewed
Published version
Åpne
Permanent lenke
https://hdl.handle.net/11250/3088632Utgivelsesdato
2023Metadata
Vis full innførselSamlinger
- Department of Informatics [917]
- Registrations from Cristin [9489]
Originalversjon
Theoretical Computer Science. 2023, 975, 114137. https://doi.org/10.1016/j.tcs.2023.114137Sammendrag
Let G be a graph. A dominating set D ⊆ V (G) is a super dominating set if for every vertex x ∈ V (G) \ D there exists y ∈ D such that NG (y) ∩ (V (G) \ D)) = {x}. The cardinality of a smallest super dominating set of G is the super domination number of G. An exact formula for the super domination number of a tree T is obtained, and it is demonstrated that a smallest super dominating set of T can be computed in linear time. It is proved that it is NP-complete to decide whether the super domination number of a graph G is at most a given integer if G is a bipartite graph of girth at least 8. The super domination number is determined for all k-subdivisions of graphs. Interestingly, in half of the cases the exact value can be efficiently computed from the obtained formulas, while in the other cases the computation is hard. While obtaining these formulas, II-matching numbers are introduced and proved that they are computationally hard to determine