Some Results On Majority Roman Domination

Abstract

A Majority Roman Dominating Function (MRDF) on
a graph G=(V,E) is a function f : V → {−1, +1, 2} satisfying the conditions that (i) the sum of its function values over at least half the closed neighborhood is at least one and (ii) every vertex u for which f(u) = −1 is adjacent to at least one vertex v for which f(v) = 2. The
weight of a MRDF is the sum of its function values over
all vertices. The Majority Roman Domination Number of
a graph G, denoted by γMR(G), is defined as γMR(G) =
min {w(f) | f is a M ajority Roman Dominating F unction of G}.
In this paper, we found some results on Majority Roman
Domination In Graphs.