RT journal article
T1 Roman Domination inWeighted Graphs
A1 Cera López, Martín
A1 García Vázquez, Pedro
A1 Valenzuela Tripodoro, Juan Carlos
A2 Matemáticas
K1 Roman domination
K1 weighted graph
K1 differential
AB 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 ∈ Vsuch that f (v) = 2. The minimum weight åv∈V f (v) of a Roman dominating function fon G is called the Roman domination number of G and is denoted by gR(G). A graphG = (V, E), together with a positive real-valued weight-function w : V → R>0, is called aweighted graph and is denoted by (G;w). The minimum weight åv∈V f (v)w(v) of a Romandominating function f on G is called the weighted Roman domination number of G andis denoted by gwR(G). The domination and Roman domination numbers of unweightedgraphs have been extensively studied, particularly for their applications in bioinformaticsand computational biology. However, graphs used to model biomolecular structures oftenrequire weights to be biologically meaningful. In this paper, we initiate the study of theweighted Roman domination number in weighted graphs. We first establish several boundsfor this parameter and present various realizability results. Furthermore, we determinethe exact values for several well-known graph families and demonstrate an equivalencebetween the weighted Roman domination number and the differential of a weighted graph.
PB MDPI
SN 2227-7390
YR 2026
FD 2026-01-29
LK http://hdl.handle.net/10498/39589
UL http://hdl.handle.net/10498/39589
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026