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Total domination and open packing in some chemical graphs. (English) Zbl 1390.92162

Summary: 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.

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C90 Applications of graph theory
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[1] M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979)
[2] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998)
[3] M.A. Henning, Packing in trees. Discrete Math. 186, 145-155 (1998) · Zbl 0957.05090 · doi:10.1016/S0012-365X(97)00228-8
[4] M.A. Henning, D. Rautenbach, P.M. Schäfer, Open packing, total domination, and the \[P_3\] P3-Radon number. Discrete Math. 313, 992-998 (2009) · Zbl 1262.05118 · doi:10.1016/j.disc.2013.01.022
[5] S. Majstorović, T. Došlić, A. Klobučar, \[KK\]-Domination on hexagonal cactus chains. Kragujev. J. Math. 36, 335-347 (2012) · Zbl 1289.05357
[6] O. Ore, Theory of Graphs (Am. Math. Soc, Providence, 1967) · Zbl 0233.10001
[7] J. Quadras, A.S.M. Mahizl, I. Rajasingh, R.S. Rajan, Domination in certain chemical graphs. J. Math. Chem. 53, 207-219 (2015) · Zbl 1307.92370 · doi:10.1007/s10910-014-0422-1
[8] D. Vukičević, A. Klobučar, \[KK\]-Dominating sets on linear benzenoids and on the infinite hexagonal grid. Croat. Chem. Acta 80, 187-191 (2007)
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