Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21283220181201Complexity and approximation ratio of semitotal domination in graphs1431501374810.22049/cco.2018.25987.1065ENZehuiShaoGuangzhou UniversityPuWuGuangzhou UniversityJournal Article20170729A 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 $2+ln(Delta-1)$.http://comb-opt.azaruniv.ac.ir/article_13748_70d5d03f125812cbc3dc8d0aec38312f.pdf