@misc{10498/33191,
year = {2024},
url = {http://hdl.handle.net/10498/33191},
abstract = {In 2016, Beeler et al. defined the double Roman domination as a variation of Roman
domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]-
Roman domination in graphs and settled some results on the triple Roman domination
case. 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 set
of neighbors of a vertex v having a positive label. In this paper we continue the study
of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the
previous 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 when
restricted to star convex and comb convex bipartite graphs and we also give sharp
bounds and exact values for several classes of graphs},
publisher = {Springer Link},
keywords = {Roman domination},
keywords = {Double Roman domination},
keywords = {Triple Roman domination},
keywords = {Quadruple Roman domination},
title = {Further Results on the [k]-Roman Domination in Graphs},
doi = {10.1007/S41980-024-00872-1},
author = {Valenzuela Tripodoro, Juan Carlos and Mateos Camacho, María Antonia and Cera López, Martín and Álvarez Ruiz, María del Pilar},
}