en تخصصي Special پژوهشي Research paper <br> <br> <br> <p></p> <div>For a graph G=(V, E) of order n, a Roman {2}-dominating function f: V&rarr;E has the property that for every vertex v in V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to least two vertices assigned 1 under f. In this paper, we classify all graphs with Roman {2}-domination number belonging to the set {2, 3, 4, n-2, n-1, n}. Furthermore, we obtain some results about Roman {2}-domination number of some graph operations.</div> Roman {2}-domination, Cartesian product, Grid graph. 117 126 http://ijmsi.ir/browse.php?a_code=A-10-4677-1&slc_lang=en&sid=1 F. Alizadeh alizadeh_faezeh@ymail.com 100319475328460010215 100319475328460010215 No Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran H. R. Maimani maimani@ipm.ir 100319475328460010216 100319475328460010216 No Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran L. Parsaei Majd leila.parsaei84@gmail.com 100319475328460010217 100319475328460010217 Yes Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran M. Rajabi Parsa mina.rparsa@gmail.com 100319475328460010218 100319475328460010218 No Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran