Critical concept for double Roman domination in graphs.

A double Roman dominating function (DRDF) on a graph G = (V , E) is a function f : V (G) → { 0 , 1 , 2 , 3 } such that (i) every vertex v with f (v) = 0 is adjacent to at least two vertices assigned a 2 or to at least one vertex assigned a 3 and (ii) every vertex v with f (v) = 1 is adjacent to at least one vertex w with f (w) ≥ 2. The weight of a DRDF is the sum of its function values over all vertices. The double Roman domination number γ dR (G) equals the minimum weight of a DRDF on G. The concept of criticality with respect to various operations on graphs has been studied for several domination parameters. In this paper, we study the concept of criticality for double Roman domination in graphs. In addition, we characterize double Roman domination edge super critical graphs and we will give several characterizations for double Roman domination vertex (edge) critical graphs. [ABSTRACT FROM AUTHOR]