“…The basic problem in this field, the Roman domination problem (RDP), was introduced by Cockayne et al in [9]. Since then, it was atracted by many scientists to theoretically study this problem on many special classes of graphs and graph structures, see [27,36,23,22,26,30,25,21], as well as algorithmically, see [17,19,20]. RDP problem for some classes of planar graphs called convex polytopes is studied in [18].…”