%0 Journal Article 
%A Valenzuela Tripodoro, Juan Carlos
%A Mateos Camacho, María Antonia
%A Cera López, Martín
%A Álvarez Ruiz, María del Pilar
%T On the Total Version of Triple Roman Domination in Graphs
%D 2025
%@ 2227-7390
%U http://hdl.handle.net/10498/38097
%X 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.
%K Roman domination
%K total Roman domination
%K triple Roman domination
%K total triple Roman domination
%~ Universidad de Cádiz