Geodesic
Associative graph products and their independence, domination and coloring numbers
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 1, pp. 53-79.

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Associative products are defined using a scheme of Imrich Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G⊗H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and irredundance. This includes Vizing's conjecture directly, and indirectly the Shannon capacity of a graph and Hedetniemi's coloring conjecture.
Keywords: graph products, independence, domination, irredundance, coloring 
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Nowakowski, Richard; Rall, Douglas. Associative graph products and their independence, domination and coloring numbers. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 1, pp. 53-79. http://geodesic.mathdoc.fr/item/DMGT_1996_16_1_a4/

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