On the equality of domination number and 2-domination numberBoruzanli Ekinci, Gülnaz (Avtor) Bujtás, Csilla (Avtor) domination number2-domination numberhereditary propertycomputational complexityThe $2$-domination number $\gamma_2(G)$ of a graph $G$ is the minimum cardinality of a set $D \subseteq V(G)$ for which every vertex outside $D$ is adjacent to at least two vertices in ▫$D$▫. Clearly, $\gamma_2(G)$ cannot be smaller than the domination number $\gamma(G)$. We consider a large class of graphs and characterize those members which satisfy $\gamma_2=\gamma$. For the general case, we prove that it is NP-hard to decide whether $\gamma_2=\gamma$ holds. We also give a necessary and sufficient condition for a graph to satisfy the equality hereditarily.20242024-10-02 14:04:18Članek v reviji163136UDK: 519.17ISSN pri članku: 1234-3099DOI: 10.7151/dmgt.2452COBISS_ID: 117087491sl