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New characterization of efficient closed and open dominated graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 15، دوره 11، شماره 4، اسفند 2026، صفحه 1235-1247 اصل مقاله (415.2 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31349.2826 | ||
| نویسندگان | ||
| Veronica Hernandez Martinez1؛ Iztok Peterin* 2، 3 | ||
| 1Universidad Carlos III de Madrid, Madrid, Spain | ||
| 2Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia | ||
| 3Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia | ||
| چکیده | ||
| 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). | ||
| کلیدواژهها | ||
| Efficient closed dominated graph؛ efficient open dominated graph؛ domination number؛ independence number؛ clique cover؛ Vizing conjecture | ||
| مراجع | ||
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