2023/02/17 by Csilla Bujtás, Bujtás, Csilla, Nima Ghanbari +3 · 1 citation
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.2302.08862
openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.