Properties of disjunctive domination in product graphs
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https://doi.org/10.26637/MJM0801/0007Abstract
In this paper properties of disjunctive domination in some graph products are studied. We examine whether disjunctive domination number is multiplicative with respect to different graph products, that is, $\gamma_2^d\left(G_1 * G_2\right) \geq$ $\gamma_2^d\left(G_1\right) \gamma_2^d\left(G_2\right)$ for all graphs $G_1$ and $G_2$ or $\gamma_2^d\left(G_1 * G_2\right) \leq \gamma_2^d\left(G_1\right) \gamma_2^d\left(G_2\right)$ for all graphs $G_1$ and $G_2$ where $*$ denotes lexicographic, tensor, strong or Cartesian product of graphs. Some other inequalities involving disjunctive domination number of product graphs and the graphs attaining these inequalities are also given.
Keywords:
Domination, disjunctive domination, disjunctive domination number, graph productMathematics Subject Classification:
Mathematics- Pages: 37-41
- Date Published: 01-01-2020
- Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)
F. Harary, Graph Theory, Addison-Wesley Publishing Co., Reading, MA/Menlo Park, CA/London, 1969.
Teresa W. Haynes, Stephen T. Hedetniemi, Peter J.Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
Sandra M Hedetniemi, Stephen T. Hedetniemi, J Knisely, D. F Rall, Secondary domination in graphs, AKCE J. Graphs Comb., 5(2008), 103-115.
Wayne Goddard, M. A Henning, Charles A McPillan, The Disjunctive Domination Number of a Graph, Quaest. Math., 37(4)(2014), 547-561.
M.A Henning, Sinclair A Marcon, Domination versus Disjunctive Domination in Graphs, Quaest. Math., 2015, $1-13$.
M. A Henning, Viroshan Naicker, Bounds on the Disjunctive Total Domination number of a Tree, Discussions Mathematicae Graph Theory, 36(2016), 153-171.
R. Hammack, W. Imrich, S. Klavzar, Handbook of Product Graphs, Discrete Mathematics and its Applications, CRC Press, Second Edition, 2011
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