RT journal article
T1 On the Total Version of Triple Roman Domination in Graphs
A1 Valenzuela Tripodoro, Juan Carlos
A1 Mateos Camacho, María Antonia
A1 Cera López, Martín
A1 Álvarez Ruiz, María del Pilar
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 Roman domination
K1 total Roman domination
K1 triple Roman domination
AB In this paper, we initiate the study of total triple Roman domination, in which we aim to ensure that each vertex of the graph is protected by at least three units, either located on itself or its neighbors, while guaranteeing that none of its neighbors remain unprotected. Formally, a total triple Roman dominating function is a labeling f of the vertices of the graph with labels {0,1,…,4} such that f(N[v])≥|AN(v)|+3, where AN(v) denotes the set of active neighbors of vertex v, i.e., those assigned a positive label. We investigate the algorithmic complexity of the associated decision problem, establish sharp bounds regarding graph structural parameters, and obtain the exact values for several graph families.
YR 2025
FD 2025
LK http://hdl.handle.net/10498/35961
UL http://hdl.handle.net/10498/35961
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026