Computational complexity aspects of super domination

Bujtás, Csilla (avtor), Ghanbari, Nima (avtor), Klavžar, Sandi (avtor)

Let $G$ be a graph. A dominating set $D\subseteq V(G)$ is a super dominating set if for every vertex $x\in V(G) \setminus D$ there exists $y\in D$ such that $N_G(y)\cap (V(G)\setminus D)) = \{x\}$. 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.

• Jezik: Angleški jezik
• Ključne besede: super domination number, trees, bipartite graphs, k-subdivision of a graph, computational complexity, matching, II-matching number, II-matchings
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: 14 str.
• Številčenje: Vol. 975, art. 114137
• PID: 20.500.12556/RUL-153123
• UDK: 519.17
• ISSN pri članku: 0304-3975
• DOI: 10.1016/j.tcs.2023.114137
• COBISS.SI-ID: 162318851
• Datum objave v RUL: 18.12.2023

Gradivo je del revije

• Naslov: Theoretical computer science
• Skrajšan naslov: Theor. comp. sci.
• Založnik: Elsevier
• ISSN: 0304-3975
• COBISS.SI-ID: 26525952

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: število super dominacije, drevesa, dvodelni grafi, k-subdivizija grafa, računska zahtevnost, prirejanje, število II-prirejanja