RT journal article
T1 Roman domination in direct product graphs and rooted product graphs1
A1 Cabrera Martínez, Abel
A1 Peterin, Iztok
A1 González Yero, Ismael
A2 Matemáticas
K1 roman domination
K1 domination
K1 direct product graph
K1 rooted product graph
AB Let G be a graph with vertex set V(G). A function f : V(G) -> {0, 1, 2) is a Roman dominating function on G if every vertex v is an element of V(G) for which f(v) = 0 is adjacent to at least one vertex u is an element of V(G) such that f(u) = 2. The Roman domination number of G is the minimum weight omega(f) = Sigma(x is an element of V(G)) f(x) among all Roman dominating functions f on G. In this article we study the Roman domination number of direct product graphs and rooted product graphs. Specifically, we give several tight lower and upper bounds for the Roman domination number of direct product graphs involving some parameters of the factors, which include the domination, (total) Roman domination, and packing numbers among others. On the other hand, we prove that the Roman domination number of rooted product graphs can attain only three possible values, which depend on the order, the domination number, and the Roman domination number of the factors in the product. In addition, theoretical characterizations of the classes of rooted product graphs achieving each of these three possible values are given.
PB AMER INST MATHEMATICAL SCIENCES-AIMS
SN 2473-6988
YR 2021
FD 2021
LK http://hdl.handle.net/10498/25712
UL http://hdl.handle.net/10498/25712
LA eng
NO The second author (Iztok Peterin) has been partially supported by the Slovenian Research Agency by the projects No. J1-1693 and J1-9109. The last author (Ismael G. Yero) has been partially supported by "Junta de Andalucia", FEDER-UPO Research and Development Call, reference number UPO1263769.
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026