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 Total domination number of central trees Bull. Korean Math. Soc.Published online August 1, 2019 Xue-gang Chen, Moo Young Sohn, and Yu-feng Wang North China Electric Power University, Changwon National University Abstract : Let $\gamma_{t}(G)$ and $\tau(G)$ denote the total domination number and vertex cover number of graph $G$, respectively. In this paper, we study the total domination number of the central tree $C(T)$ for a tree $T$. First, a relationship between the total domination number of $C(T)$ and the vertex cover number of tree $T$ are discussed. We characterize the central trees with equal total domination number and independent number. Applying the first result, we improved the upper bound on the total domination number of $C(T)$ and solved one open problem posed by Kazemnejad et al.. Keywords : Total domination number, vertex cover number, cental tree. MSC numbers : 05C69, 05C35 Full-Text :