Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TOTAL DOMINATION NUMBER OF CENTRAL TREES

  • Chen, Xue-Gang (Department of Mathematics North China Electric Power University) ;
  • Sohn, Moo Young (Department of Mathematics Changwon National University) ;
  • Wang, Yu-Feng (Department of Mathematics North China Electric Power University)
  • Received : 2019.02.10
  • Accepted : 2019.07.08
  • Published : 2020.01.31
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Abstract

Let γt(G) and τ(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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References

  1. E. J. Cockayne, R. M. Dawes, and S. T. Hedetniemi, Total domination in graphs, Net-works 10 (1980), no. 3, 211-219. https://doi.org/10.1002/net.3230100304
  2. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs, Monographs and Textbooks in Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998.
  3. T. W. Haynes, Domination in graphs, Monographs and Textbooks in Pure and Applied Mathematics, 209, Marcel Dekker, Inc., New York, 1998.
  4. M. A. Henning and A. Yeo, Total domination in graphs, Springer Monographs in Mathematics, Springer, New York, 2013. https://doi.org/10.1007/978-1-4614-6525-6
  5. F. Kazemnejad and S. Moradi, Total domination number of central graphs, Bull. Korean Math. Soc. 56 (2019), no. 4, 1059-1075. https://doi.org/10.4134/BKMS.b180891
  6. K. Thilagavathi, J. V. Vivin, and B. Anitha. Circumdetic graphs, Far East J. Appl. Math. 26 (2007), no. 2, 191-201.