Geodesic
The well-covered dimension of products of graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 811-827

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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 K_n × G is found, provided that G has a largest greedy independent decomposition of length c lt; 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.
Keywords: well-covered dimension, maximal independent sets 
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Birnbaum, Isaac; Kuneli, Megan; McDonald, Robyn; Urabe, Katherine; Vega, Oscar. The well-covered dimension of products of graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 811-827. http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a10/