Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 New Characterization of Efficient Closed and Open Dominated Graphs 1235 1247 15176 10.22049/cco.2026.31349.2826 EN Veronica Hernandez Martinez Universidad Carlos III de Madrid, Madrid, Spain Iztok Peterin Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia Journal Article 2025 12 20 A graph $G$ is an efficient closed dominated graph (ECD-graph) if there exists a subset of vertices whose closed neighborhoods partition $V(G)$ and is an efficient open dominated graph (EOD-graph) if there exists a subset of vertices whose open neighborhoods partition $V(G)$. We present a new characterization of ECD- and EOD-graphs that involves independent number and a vertex clique cover of some family of cliques of closed neighborhood graph and open neighborhood graph, respectively, that are intersection graphs of closed and open neighborhoods, respectively. Several consequences are presented as well, one of them with respect to the Vizing's conjecture and the other solves a conjecture on EOD-graphs among toruses $C_t\Box C_r$ posed by Kuziak et al. (Discrete Math. Theoret. Comput. Sci. 16 (2014) 105-120). https://comb-opt.azaruniv.ac.ir/article_15176_1e8c4feddd383909a6c419b363c14461.pdf