20.500.12556/DiRROS-18642 Graphs with equal Grundy domination and independence number The 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. Grundy domination independence number upper domination number bipartite graphs Grundyjeva dominacija neodvisnostno število zgornje dominantno število dvodelni grafi true false true Angleški jezik Slovenski jezik Neznano 2024-04-09 10:12:21 2024-04-09 10:12:22 2024-04-10 03:38:22 0000-00-00 00:00:00 2023 0 0 art. 100777 (15 str.) iss. 2 Vol. 48 May 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-05-01 519.17 1572-5286 10.1016/j.disopt.2023.100777 154012931 1-s2.0-S1572528623000191-main.pdf 1-s2.0-S1572528623000191-main.pdf 1 4AEB000C0E70536E98789402FA20E358 4461ae84ad213894b477955154c22457f474983d8aedca1df00517082bc9a80a 8d2cd735-f638-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25457 https://www.sciencedirect.com/science/article/pii/S1572528623000191 1 21a9bb66-f638-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25456 Inštitut za matematiko, fiziko in mehaniko 0 0 0