Geodesic
Arithmetically maximal independent sets in infinite graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 167-182

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Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.
Keywords: infinite graph, independent set, arithmetical maximal set, line graph 
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Bylka, Stanisław. Arithmetically maximal independent sets in infinite graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 167-182. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a16/