@misc{10498/35960,
year = {2024},
month = {12},
url = {http://hdl.handle.net/10498/35960},
abstract = {Domination in graphs is a widely studied field, where many different definitions have been introduced
in the last years to respond to different network requirements. This paper presents a new dominating
parameter based on the well-known strong Roman domination model. Given a positive integer $p$, we call
a $p$-strong Roman domination function ($p$-StRDF) in a graph $G$ to a function
$f:V(G)\rightarrow  \{0,1,2, \ldots , \left\lceil \frac{\Delta+p}{p} \right\rceil \}$ having the
property that if $f(v)=0$, then there is a vertex $u\in N(v)$ such that $f(u) \ge 1+ \left\lceil
\frac{|B_0\cap N(u)|}{p} \right\rceil $, where $B_0$ is the set of vertices with label $0$. The
$p$-strong Roman domination number $\gamma_{StR}^p(G)$ is the minimum weight (sum of labels) of a
$p$-StRDF on $G$. We study the NP-completeness of the \emph{$p$-StRD}-problem, we also
provide general and tight upper and lower bounds depending on several classical invariants of the graph
and, finally, we determine the exact values for some families of graphs.},
keywords = {graph},
keywords = {NP-complete problem},
keywords = {domination},
keywords = {Roman domination},
keywords = {strong Roman domination},
keywords = {p-strong Roman domination},
title = {p-Strong Roman Domination in Graphs},
doi = {DOI:10.37394/23206.2024.23.104},
author = {Valenzuela Tripodoro, Juan Carlos and Mateos Camacho, María Antonia and Álvarez Ruiz, María del Pilar and Cera López, Martín and Moreno Casablanca, Rocio},
}