Packing and Domination Invariants on Cartesian Products and Direct Products
نویسنده
چکیده
The dual notions of domination and packing in finite simple graphs were first extensively explored by Meir and Moon in [15]. Most of the lower bounds for the domination number of a nontrivial Cartesian product involve the 2-packing, or closed neighborhood packing, number of the factors. In addition, the domination number of any graph is at least as large as its 2-packing number, and the invariants have the same value for any tree. In this paper we survey what is known about the domination, total domination and paired-domination numbers of Cartesian products and direct products. In the process we highlight two other packing invariants that each play a role similar to that played by the 2-packing number in dominating Cartesian products.
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