%0 Journal Article 
%A Valenzuela Tripodoro, Juan Carlos
%A Mateos Camacho, María Antonia
%A Álvarez Ruiz, María del Pilar
%A Cera López, Martín
%A Moreno Casablanca, Rocio
%T p-Strong Roman Domination in Graphs
%D 2024
%U http://hdl.handle.net/10498/35960
%X 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.
%K graph
%K NP-complete problem
%K domination
%K Roman domination
%K strong Roman domination
%K p-strong Roman domination
%~ Universidad de Cádiz