The Roman domination number of some special classes of graphs - convex polytopes

Abstract

In this paper we study the Roman domination number of some classes of planar graphs - convex polytopes: An, Rn and Tn. We establish the exact values of Roman domination number for: An, R3k, R3k+1, T8k, T8k+2, T8k+3, T8k+5 and T8k+6. For R3k+2, T8k+1, T8k+4 and T8k-1 we propose new upper and lower bounds, proving that the gap between the bounds is 1 for all cases except for the case of T8k+4, where the gap is 2.