Journal of Mathematical Chemistry

, Volume 56, Issue 5, pp 1481–1492 | Cite as

Total domination and open packing in some chemical graphs

  • Yingying Gao
  • Enqiang Zhu
  • Zehui Shao
  • Ivan Gutman
  • Antoaneta Klobučar
Original Paper


In this paper we obtain some bounds and exact values of the total domination numbers and open packing numbers for pyrene torus, hexabenzocoronene, H-phenylenic nanotube and H-napthelenic nanotube.


Domination number Packing number Benzenoid system Benzenoid torus Nanotube Molecular graph 

Mathematics Subject Classification

05C69 05C90 92E10 



This work was supported by the National Key Research and Development Program under Grant 2017YFB0802300, the National Natural Science Foundation of China under the Grants 61309015, 61672501, and Applied Basic Research (Key Project) of Sichuan Province under the Grant 2017JY0095.


  1. 1.
    M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979)Google Scholar
  2. 2.
    T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998)Google Scholar
  3. 3.
    M.A. Henning, Packing in trees. Discrete Math. 186, 145–155 (1998)CrossRefGoogle Scholar
  4. 4.
    M.A. Henning, D. Rautenbach, P.M. Schäfer, Open packing, total domination, and the \(P_3\)-Radon number. Discrete Math. 313, 992–998 (2009)CrossRefGoogle Scholar
  5. 5.
    S. Majstorović, T. Došlić, A. Klobučar, \(K\)-Domination on hexagonal cactus chains. Kragujev. J. Math. 36, 335–347 (2012)Google Scholar
  6. 6.
    O. Ore, Theory of Graphs (Am. Math. Soc, Providence, 1967)Google Scholar
  7. 7.
    J. Quadras, A.S.M. Mahizl, I. Rajasingh, R.S. Rajan, Domination in certain chemical graphs. J. Math. Chem. 53, 207–219 (2015)CrossRefGoogle Scholar
  8. 8.
    D. Vukičević, A. Klobučar, \(K\)-Dominating sets on linear benzenoids and on the infinite hexagonal grid. Croat. Chem. Acta 80, 187–191 (2007)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Institute of Intelligence SoftwareGuangzhou UniversityGuangzhouChina
  2. 2.Faculty of ScienceUniversity of KragujevacKragujevacSerbia
  3. 3.Department of Mathematics, Faculty of EconomicsUniversity of OsijekOsijekCroatia

Personalised recommendations