A characterization of double Roman trees

Michael A. Henning | Nader Jafari Rad

---

URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=106011
Date :  2019/01/12
Publish in :    Discrete Applied Mathematics
DOI :  https://doi.org/10.1016/j.dam.2018.12.033
Link :  https://www.sciencedirect.com/science/article/pii/S0166218X19300095
Keywords :,Double Roman dominating function,double, trees

Abstract :

---

A double Roman dominating function on a graph is a function having the property that every vertex of weight 0 under has at least one neighbor of weight 3 under or at least two neighbors of weight 2 under and every vertex of weight 1 under has at least one neighbor of weight at least 2 under . The weight of a double Roman dominating function is the sum of the weights of the vertices. The double Roman domination number of , denoted , is the minimum weight of a double Roman dominating function in . For every graph , , where denotes the domination number of . A graph satisfying is a double Roman graph. In this paper, we characterize the double Roman trees, which answers a problem posed by Beeler et al. (2016).