Weak Roman domination in graphs
T. N. M. Malini Mai, P. Roushini Leely Pushpam · Discussiones Mathematicae Graph Theory · 2011
0(w) = f(w) if w 2 V − fu,vg, has no undefended vertex. The weight of f is w(f) = P v2V f(v). The weak Roman domination number, denoted by r(G), is the minimum weight of a WRDF in G. In this paper, we characterize the class of trees and split graphs for which r(G) = (G) and find r-value for a caterpillar, a 2 � n grid graph and a complete binary tree.