Italian domination in rooted product graphs
R. Hernandez-Ortiz, L. P. Montejano, J. A. Rodriguez-Velazquez
TL;DR
This paper derives formulas for the Italian domination number in rooted product graphs and corona graphs, and proves that computing this number is NP-hard, highlighting the problem's computational complexity.
Contribution
The paper provides closed-form formulas for the Italian domination number in rooted product and corona graphs, and establishes NP-hardness of the problem.
Findings
Closed formulas for rooted product graphs
Formulas for corona graphs
NP-hardness of computing Italian domination number
Abstract
In this article, we obtain closed formulae for the Italian domination number of rooted product graphs. As a particular case of the study, we derive the corresponding formulas for corona graphs, and we provide an alternative proof that the problem of computing the Italian domination number of a graph is NP-hard.
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