On independent and total variants of Roman and Italian domination in Mycielskian graphs

Abel Cabrera-Martínez; Alfonso Ríder Moyano; Ismael Rios-Villamar; Abel Cabrera-Martínez; Alfonso Ríder Moyano; Ismael Rios-Villamar

doi:10.3934/math.2026717

AIMS Mathematics

2026, Volume 11, Issue 6: 17550-17563. doi: 10.3934/math.2026717

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Research article

On independent and total variants of Roman and Italian domination in Mycielskian graphs

1.
Departamento de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071, Córdoba, Spain
2.
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame 54, Col. La Garita 39650, Acapulco, Guerrero, Mexico

Received: 15 January 2026 Revised: 04 June 2026 Accepted: 10 June 2026 Published: 17 June 2026
MSC : 05C69, 05C76

Let $ G $ be a graph and $ \mu(G) $ its Mycielskian graph. Roman and Italian domination, together with their independent and total variants, have been extensively studied, including studies on graph operators and products. In this article, we investigated the behavior of these domination parameters in Mycielskian graphs and, in particular, we provided closed formulas for these invariants in $ \mu(G) $ in terms of the corresponding values of $ G $.
- Roman domination,
- Italian domination,
- Mycielskian graphs
Citation: Abel Cabrera-Martínez, Alfonso Ríder Moyano, Ismael Rios-Villamar. On independent and total variants of Roman and Italian domination in Mycielskian graphs[J]. AIMS Mathematics, 2026, 11(6): 17550-17563. doi: 10.3934/math.2026717

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Abstract

Let $ G $ be a graph and $ \mu(G) $ its Mycielskian graph. Roman and Italian domination, together with their independent and total variants, have been extensively studied, including studies on graph operators and products. In this article, we investigated the behavior of these domination parameters in Mycielskian graphs and, in particular, we provided closed formulas for these invariants in $ \mu(G) $ in terms of the corresponding values of $ G $.

References

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