• Korean Journal of Mathematics
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• v.7 no.1
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• pp.37-44
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• 1999

We study the relations among the domination number, the independent domination number, and the independence number of an oriented tree and establish their bounds. We also do the same for a binary tree.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.17-25
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• 2021

A set D ⊆ V (G) is an independent transversal dominating set of G if D is a dominating set and also intersects every maximum independent set in G. The minimum cardinality of such a set is equal to the transversal domination number, denoted by ��it(G). This paper is devoted to the computation of the independent transversal domination number of some complementary prism.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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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 the Korean Mathematical Society
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• v.39 no.2
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.