Semitotal Roman Domination in Graphs

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 is an element of V(G) with f(v)=0, there exists u is an element of V(G) for which f(u)=2 and uv is an element of E(G) and for each v is an element of V(G) with f(v)not equal 0, there exists u is an element of V(G) for which f(u)not equal 0 and d(G)(u,v)<= 2. The minimum weight omega(G)(f) = & sum;(u is an element of V(G))f(u) of a semitotal Roman dominating function f of G is the semitotal Roman domination number} of G, denoted by gamma(t2R)(G). In this paper, we initiate the study of semitotal Roman domination. We characterize graphs G with small values of gamma(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.