RT journal article
T1 On the strong Roman domination number of graphs
A1 Álvarez Ruiz, María del Pilar
A1 Mediavilla Gradolph, T.
A1 Sheikholeslami, S.M.
A1 Valenzuela Tripodoro, Juan Carlos
A1 González Yero, Ismael
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 Domination
K1 Roman domination
K1 Roman domination number
K1 Strong Roman domination
AB Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a “stronger” neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph G=(V,E), is a function f:V→{0,1,2} such that every vertex v with f(v)=0 has at least a neighbor w in G for which f(w)=2. The Roman domination number of a graph is the minimum weight, ∑v∈Vf(v), of a Roman dominating function. In this paper we initiate the study of a new parameter related to Roman domination, which we call strong Roman domination number and denote it by γStR(G). We approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. In particular, we first show that the decision problem regarding the computation of the strong Roman domination number is NP-complete, even when restricted to bipartite graphs. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, we prove that for any tree T of order n≥3, γStR(T)≤6n/7 and characterize all extremal trees.
PB Elsevier
SN 0166-218X
YR 2017
FD 2017
LK http://hdl.handle.net/10498/33937
UL http://hdl.handle.net/10498/33937
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026