Semitotal Roman Domination in Graphs (European Journal of Pure and Applied Mathematics, 2025)
Let $G$ be a nontrivial graph without isolated vertices. A function $f:V(G) → \{0,1,2\}$ is a semitotal Roman dominating function of $G$ if for each $v\in V(G)$ with $f(v)=0$, there exists $u\in V(G)$ for which $f(u)=2$ and $uv\in E(G)$ and for each $v \in V(G)$ with $f(v) eq 0$, there exists $u\in V(G)$ for which $f(u) eq 0$ and $d_G(u,v)\le 2$. The minimum weight $ω_G(f)=\sum_{u\in V(G)}f(u)$ of a semitotal Roman dominating function $f$ of $G$ is the semitotal Roman domination number of $G$, denoted by $γ_{t2R}(G)$. In this paper, we initiate the study of semitotal Roman domination. We characterize graphs $G$ with small values of $γ_{t2R}(G)$ and solve some realization problems with other existing related concepts. We also investigate the semitotal Roman domination in the join, corona, and complimentary prism of graphs.
Keywords: Roman Domination; Semitotal Domination; Total Domination; Semitotal Roman Domination