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Research Article | Open Access

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

Abel Cabrera-Martínez1( ), Alfonso Ríder Moyano1, Ismael Rios-Villamar2
Departamento de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071, Córdoba, Spain
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame 54, Col. La Garita 39650, Acapulco, Guerrero, Mexico
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Abstract

Let G be a graph and μ ( 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 μ ( G ) in terms of the corresponding values of G.

Keywords

Roman dominationItalian dominationMycielskian graphs
CLC number: 05C69, 05C76

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AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 17550-17563
DOI: 10.3934/math.2026717

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Cabrera-Martínez A, Moyano AR, Rios-Villamar I. On independent and total variants of Roman and Italian domination in Mycielskian graphs. AIMS Mathematics, 2026, 11(6): 17550-17563. https://doi.org/10.3934/math.2026717

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Received: 15 January 2026
Revised: 04 June 2026
Accepted: 10 June 2026
Published: 15 June 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)