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New Characterization of Efficient Closed and Open Dominated Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 خرداد 1405 | ||
| نوع مقاله: Special issue of CCO to honor Odile Favaron | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31349.2826 | ||
| نویسندگان | ||
| Iztok Peterin* 1؛ Veronica I Hernandez Martinez2 | ||
| 1University of Maribor | ||
| 2Universidad Carlos III de Madrid, Madrid, Spain | ||
| 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 | ||
| domination number؛ independence number؛ clique cover؛ Vizing conjecture | ||
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آمار تعداد مشاهده مقاله: 7 |
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