@misc{10498/39589,
year = {2026},
month = {1},
url = {http://hdl.handle.net/10498/39589},
abstract = {A Roman dominating function for a (non-weighted) graph G = (V, E) is a function f :
V → {0, 1, 2} such that every vertex u ∈ V with f (u) = 0 has at least one neighbor v ∈ V
such that f (v) = 2. The minimum weight åv∈V f (v) of a Roman dominating function f
on G is called the Roman domination number of G and is denoted by gR(G). A graph
G = (V, E), together with a positive real-valued weight-function w : V → R>0, is called a
weighted graph and is denoted by (G;w). The minimum weight åv∈V f (v)w(v) of a Roman
dominating function f on G is called the weighted Roman domination number of G and
is denoted by gwR(G). The domination and Roman domination numbers of unweighted
graphs have been extensively studied, particularly for their applications in bioinformatics
and computational biology. However, graphs used to model biomolecular structures often
require weights to be biologically meaningful. In this paper, we initiate the study of the
weighted Roman domination number in weighted graphs. We first establish several bounds
for this parameter and present various realizability results. Furthermore, we determine
the exact values for several well-known graph families and demonstrate an equivalence
between the weighted Roman domination number and the differential of a weighted graph.},
publisher = {MDPI},
keywords = {Roman domination},
keywords = {weighted graph},
keywords = {differential},
title = {Roman Domination inWeighted Graphs},
doi = {10.3390/math14030466},
author = {Cera López, Martín and García Vázquez, Pedro and Valenzuela Tripodoro, Juan Carlos},
}