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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1023,
author = {Richard J. Nowakowski and Douglas F. Rall},
title = {Associative graph products and their independence, domination and coloring numbers},
journal = {Discussiones Mathematicae Graph Theory},
volume = {16},
year = {1996},
pages = {53-79},
zbl = {0865.05071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1023}
}
Richard J. Nowakowski; Douglas F. Rall. Associative graph products and their independence, domination and coloring numbers. Discussiones Mathematicae Graph Theory, Tome 16 (1996) pp. 53-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1023/
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