@misc{10498/38097,
year = {2025},
month = {4},
url = {http://hdl.handle.net/10498/38097},
abstract = {In this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from (Formula presented.) to the vertices of a graph such that every vertex is protected by at least three units either on itself or its neighbors while ensuring that none of its neighbors remains unprotected. Formally, a total triple Roman dominating function is a function (Formula presented.) such that (Formula presented.), where (Formula presented.) 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.},
publisher = {Multidisciplinary Digital Publishing Institute (MDPI)},
keywords = {Roman domination},
keywords = {total Roman domination},
keywords = {triple Roman domination},
keywords = {total triple Roman domination},
title = {On the Total Version of Triple Roman Domination in Graphs},
doi = {10.3390/MATH13081277},
author = {Valenzuela Tripodoro, Juan Carlos and Mateos Camacho, María Antonia and Cera López, Martín and Álvarez Ruiz, María del Pilar},
}