(untitled) (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 vV(G) with f(v)=0, there exists uV(G) for which f(u)=2 and uvE(G) and for each v V(G) with f(v) eq 0, there exists uV(G) for which f(u) eq 0 and d_G(u,v)2. The minimum weight ω_G(f)=_uV(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.