Double Roman domination in some graphs

A double Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions that if [Formula: see text], then every vertex v is adjacent to minimum one vertex u for which [Formula: see text] or two vertices [Formula: see text] and [Formula: see text] for which [Formula: see text] and if [Formula: see text], then v is adjacent to minimum one vertex [Formula: see text] for which [Formula: see text] or 2. The weight of a double Roman dominating function denoted as [Formula: see text] is defined as [Formula: see text]. The double Roman domination number denoted as [Formula: see text] is the minimum weight of double Roman dominating function on G. In this paper, we determine the [Formula: see text]-value of some graphs such as Comb, Closed Helm, Comet, Double Comet, Lollipop, Helm, Double Comb and Jelly fish graphs.