A restrained Roman dominating function (RRD-function) on a graph \(G=(V,E)\) is \(f\) from \(V\) into \(\{0,1,2\}\) satisfying: (i) every vertex \(u\) with \(f(u)=0\) adjacent to \(v\) \(f(v)=2\); (ii) the subgraph induced by vertices assigned 0 under has no isolated vertices. The weight of an RRD-function sum its value over whole set vertices, and domination number minimum \(G.\) In this paper...