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Complexity and approximation ratio of semitotal domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 3، شماره 2، اسفند 2018، صفحه 143-150 اصل مقاله (334.87 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.25987.1065 | ||
| نویسندگان | ||
| Zehui Shao* ؛ Pu Wu | ||
| Guangzhou University | ||
| چکیده | ||
| A set $S \subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ and every vertex in $S$ is within distance 2 of another vertex of $S$. The semitotal domination number $\gamma_{t2}(G)$ is the minimum cardinality of a semitotal dominating set of $G$. We show that the semitotal domination problem is APX-complete for bounded-degree graphs, and the semitotal domination problem in any graph of maximum degree $\Delta$ can be approximated with an approximation ratio of $2+\ln(\Delta-1)$. | ||
| کلیدواژهها | ||
| semitotal domination؛ APX-complete؛ NP-completeness | ||
| مراجع | ||
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[8] E. Zhu, Z. Shao, and J. Xu, Semitotal domination in claw-free cubic graphs, Graphs Combin. 33 (2017), no. 5, 1119–1130. | ||
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