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Discussiones Mathematicae Graph Theory 30(3) (2010) 425-435
DOI: https://doi.org/10.7151/dmgt.1504

A CHARACTERIZATION OF (γ_t,γ₂)-TREES

You Lu,  Xinmin Hou,  Jun-Ming Xu  and  Ning Li

Department of Mathematics
University of Science and Technology of China
Hefei, Anhui, 230026, China
e-mail: xmhou@ustc.edu.cn

Abstract

Let γ_t(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γ_t(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

Keywords: domination, total domination, 2-domination, (λ,μ)-tree.

2010 Mathematics Subject Classification: 05C69.

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Received 27 February 2009
Revised 28 July 2009
Accepted 1 September 2009