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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 $T$ is discussed. We characterize the central trees with equal total domination number and independence number. Applying the first result, we improve the upper bound on the total domination number of $C(T)$ and solve one open problem posed by Kazemnejad et al..
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참고문헌 (6)
참고문헌 신청
E. J. Cockayne / 1980 / Total domination in graphs / Networks 10(3):211~219
T. W. Haynes / 1998 / Fundamentals of domination in graphs / Marcel Dekker, Inc
T. W. Haynes / 1998 / Domination in graphs / Marcel Dekker, Inc
M. A. Henning / 2013 / Total domination in graphs, Springer Monographs in Mathematics / Springer
Farshad Kazemnejad / 2019 / Total domination number of central graphs / 대한수학회보 56(4):1059~1075
T. W. Haynes / 1998 / Fundamentals of domination in graphs / Marcel Dekker, Inc
T. W. Haynes / 1998 / Domination in graphs / Marcel Dekker, Inc
M. A. Henning / 2013 / Total domination in graphs, Springer Monographs in Mathematics / Springer
Farshad Kazemnejad / 2019 / Total domination number of central graphs / 대한수학회보 56(4):1059~1075
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