Majority double Roman domination in graphs

A majority double Roman dominating function (MDRDF) on a graph G = (V, E) is a function f : V -> {-1, +1,2, 3} such that (i) every vertex v with f(v) = -1 is adjacent to at least two vertices assigned with 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is adjacent to at least one vertex w with f(w) >= 2 and (iii) Sigma(u is an element of N[v]) f (u) >= 1, for at least half of the vertices in G. The weight of an MDRDF is the sum of its function values over all vertices. The majority double Roman domination number of a graph G, denoted by (gamma MDR)(G), is defined as (gamma MDR)(G) = min{w(f) | f is an MDRDF of G}. In this paper, we introduce and study the majority double Roman domination number on some classes of graphs.