# Trees With Equal Roman {2}-domination Number And Independent Roman {2}-domination Number

Pu Wu, Z. Li, Zehui Shao, S. M. Sheikholeslami
Published 2019 · Mathematics, Computer Science

A Roman {2}-dominating function (R{2}DF) on a graph G  =(V , E ) is a function f  : V  → {0, 1, 2} satisfying the condition that every vertex u for which f (u ) = 0 is adjacent to either at least one vertex v with f (v ) = 2 or two vertices v 1 , v 2 with f (v 1 ) = f (v 2 ) = 1. The weight of an R{2}DF f is the value w (f ) = ∑u∈V f (u ). The minimum weight of an R{2}DF on a graph G is called the Roman {2}-domination number γ{R 2} (G ) of G . An R{2}DF f is called an independent Roman {2}-dominating function (IR{2}DF) if the set of vertices with positive weight under f is independent. The minimum weight of an IR{2}DF on a graph G is called the independent Roman {2}-domination number i {R 2} (G ) of G. In this paper, we answer two questions posed by Rahmouni and Chellali.
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