Modern roman domination in graphs

الملخص EN

In this paper, “a Modern Roman Domination" is introduced, which is a new model of graph domination.

A modem Roman dominating function on a graph G = (V; E) is a labeling function/: V(G) — {0.1.2.3} such that every vertex with label 0 is adjacent to two vertices, one of them of label 2 and the other of label 3 .And every vertex with label 1 is adjacent to a vertex with label 2 or 3.

The weight of a modem Roman dominating function /is w(f) = Spev/(v).The "Modem Roman Domination Number"ymr(G) is the minimum f(V) = E„ev f(v) over all such functions ofG.

In this paper, some properties of this new model of graph domination are introduced.