On the Total Version of Triple Roman Domination in Graphs
In this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0, 1, 2, 3, 4} 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 it...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/174167 |
| Acceso en línea: | https://hdl.handle.net/11441/174167 https://doi.org/10.3390/math13081277 |
| Access Level: | acceso abierto |
| Palabra clave: | Roman domination total Roman domination triple Roman domination total triple Roman domination |
| Sumario: | In this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0, 1, 2, 3, 4} 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 f : V(G) → {0, 1, 2, 3, 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. |
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