• 대한수학회논문집
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• 제18권1호
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• pp.181-192
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• 2003

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

• 대한수학회지
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• 제41권5호
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.883-896
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• 2022

A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".