@article{Zhang2024, 
author = {Mingyu Zhang and Junxia Zhang},
title = {On Roman balanced domination of graphs},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36001-36011},
keywords = {Roman balanced dominating function, Roman balanced domination number, Rd-balanced graph},
url = {https://www.sciopen.com/article/10.3934/math.20241707},
doi = {10.3934/math.20241707},
abstract = {Let  G be a graph with vertex set  V. A function  f :  V→{−1,0,2} is called a Roman balanced dominating function (RBDF) of  G if  ∑u∈NG[v]f(u)=0 for each vertex  v∈V. The maximum (resp. minimum) Roman balanced domination number  γRbM(G) (resp.  γRbm(G)) is the maximum (resp. minimum) value of  ∑v∈Vf(v) among all Roman balanced dominating functions  f. A graph  G is called  Rd-balanced if  γRbM(G)=γRbm(G)=0. In this paper, we obtain several upper and lower bounds on  γRbM(G) and  γRbm(G) and further determine several classes of  Rd-balanced graphs.}
}