Discussiones Mathematicae Graph Theory 16(1) (1996) 53-79
doi: 10.7151/dmgt.1023

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Richard J. Nowakowski

Dalhousie University, Halifax, Nova Scotia, Canada B3J 3J5

Douglas F. Rall

Furman University, Greenville, SC 29613 U.S.A.


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.

1991 Mathematics Subject Classification: 05C99.


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