RT journal article
T1 Further Results on the [k]-Roman Domination in Graphs
A1 Valenzuela Tripodoro, Juan Carlos
A1 Mateos Camacho, María Antonia
A1 Cera López, Martín
A1 Álvarez Ruiz, María del Pilar
K1 Roman domination
K1 Double Roman domination
K1 Triple Roman domination
K1 Quadruple Roman domination
AB In 2016, Beeler et al. defined the double Roman domination as a variation of Romandomination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]-Roman domination in graphs and settled some results on the triple Roman dominationcase. In 2022, Amjadi et al. studied the quadruple version of this Roman-domination-type problem. Given any labeling of the vertices of a graph, AN (v) stands for the setof neighbors of a vertex v having a positive label. In this paper we continue the studyof the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with theprevious versions when 2 ≤ k ≤ 4. Namely, f is a [k]-RDF if f (N [v]) ≥ k +|AN (v)|for all v. We prove that the associate decision problem is NP-complete even whenrestricted to star convex and comb convex bipartite graphs and we also give sharpbounds and exact values for several classes of graphs
PB Springer Link
SN 1735-8515
YR 2024
FD 2024
LK http://hdl.handle.net/10498/33191
UL http://hdl.handle.net/10498/33191
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026