Further results on independent double roman trees

Abstract

AbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a DRDF is the sum of its function values over all vertices. A DRDF f is an independent double Roman dominating function (IDRDF) if the set of vertices assigned 1, 2 and 3 is independent. The independent double Roman domination number [Formula: see text] is the minimum weight over all IDRDFs of G. Every graph G satisfies [Formula: see text] where i(G) is the independent domination number. In this paper, we give a characterization of all trees T with [Formula: see text]

Keywords

• Independent double Roman domination
• independent domination
• trees
• 05C69
• 05C05