RT journal article
T1 Dominating the Direct Product of Two Graphs through Total Roman Strategies
A1 Cabrera Martínez, Abel
A1 Kuziak, Dorota
A1 Peterin, Iztok
A1 González Yero, Ismael
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 total Roman domination
K1 Roman domination
K1 direct product graphs
AB Given a graphGwithout isolated vertices, a total Roman dominating function forGis a function f:V(G)->{0,1,2}such that every vertexuwithf(u)=0is adjacent to a vertexvwithf(v)=2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number gamma tR(G)ofGis the smallest possible value of n-ary sumation v is an element of V(G)f(v)among all total Roman dominating functionsf. The total Roman domination number of the direct productGxHof the graphsGandHis studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between gamma tR(GxH)and some classical domination parameters for the factors are given. Characterizations of the direct product graphsGxHachieving small values (<= 7) for gamma tR(GxH)are presented, and exact values for gamma tR(GxH)are deduced, while considering various specific direct product classes.
PB MDPI
SN 2227-7390
YR 2020
FD 2020-09
LK http://hdl.handle.net/10498/24034
UL http://hdl.handle.net/10498/24034
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026