Complexity and exact values for []-Roman and strong Roman domination for specific graph families
Motivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks. A Roman dominating function (RDF) is a labeling of the vertices of a graph with labels...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::f0bbeea5d4f6c7282f686bb20392be0c |
| Acceso en línea: | https://hdl.handle.net/11441/186763 https://doi.org/10.3390/math14091535 |
| Access Level: | acceso abierto |
| Palabra clave: | Roman domination Triple Roman domination Strong Roman domination [k]-Roman domination |
| Sumario: | Motivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks. A Roman dominating function (RDF) is a labeling of the vertices of a graph with labels in {0,1,2} such that every vertex labeled 0 is adjacent to at least one vertex labeled 2. The weight of an RDF is the sum of all vertex labels. Vertices labeled 2 are intended to protect their neighbors labeled 0. The Roman domination number is the minimum weight of an RDF on the graph. In 2017, Álvarez et al. introduced strong Roman domination as a variant of Roman domination designed to protect the vertices of a graph against multiple simultaneous attacks. In 2021, Ahangar et al. defined [] -Roman domination, another model intended to defend a graph against individual attacks on vertices. In this paper, we investigate the computational complexity of the associated decision problems for [] -Roman domination and strong Roman domination. Furthermore, we determine exact values of these parameters for several graph families under both variants. |
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