We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of Kn × G is found, provided that G has a largest greedy independent decomposition of length c < n. Formulae to find the well-covered dimension of graphs obtained by vertex blowups on a known graph, and to the lexicographic product of two known graphs are also given.
@article{bwmeta1.element.doi-10_7151_dmgt_1770,
author = {Isaac Birnbaum and Megan Kuneli and Robyn McDonald and Katherine Urabe and Oscar Vega},
title = {The Well-Covered Dimension Of Products Of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {811-827},
zbl = {1303.05164},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1770}
}
Isaac Birnbaum; Megan Kuneli; Robyn McDonald; Katherine Urabe; Oscar Vega. The Well-Covered Dimension Of Products Of Graphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 811-827. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1770/
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