Graphs with equal Grundy domination and independence numberBacsó, Gábor (Avtor) Brešar, Boštjan (Avtor) Kuenzel, Kirsti (Avtor) Rall, Douglas F. (Avtor) Grundy dominationindependence numberupper domination numberbipartite graphsThe Grundy domination number, ${\gamma_{\rm gr}}(G)$, of a graph $G$ is the maximum length of a sequence $(v_1,v_2,\ldots, v_k)$ of vertices in $G$ such that for every $i\in \{2,\ldots, k\}$, the closed neighborhood $N[v_i]$ contains a vertex that does not belong to any closed neighborhood $N[v_j]$, where $j<i$. It is well known that the Grundy domination number of any graph $G$ is greater than or equal to the upper domination number $\Gamma(G)$, which is in turn greater than or equal to the independence number $\alpha(G)$. In this paper, we initiate the study of the class of graphs $G$ with $\Gamma(G)={\gamma_{\rm gr}}(G)$ and its subclass consisting of graphs $G$ with $\alpha(G)={\gamma_{\rm gr}}(G)$. We characterize the latter class of graphs among all twin-free connected graphs, provide a number of properties of these graphs, and prove that the hypercubes are members of this class. In addition, we give several necessary conditions for graphs $G$ with $\Gamma(G)={\gamma_{\rm gr}}(G)$ and present large families of such graphs.20232024-04-09 10:12:21Neznano18642UDK: 519.17ISSN pri članku: 1572-5286DOI: 10.1016/j.disopt.2023.100777COBISS_ID: 154012931sl