Geodesic
Distance independence in graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 397-409.

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For a set D of positive integers, we define a vertex set S ⊆ V(G) to be D-independent if u, v ∈ S implies the distance d(u,v) ∉ D. The D-independence number β_D(G) is the maximum cardinality of a D-independent set. In particular, the independence number β(G) = β_1(G). Along with general results we consider, in particular, the odd-independence number β_ODD(G) where ODD = 1,3,5,....
Keywords: independence number, distance set 
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Sewell, J.; Slater, Peter. Distance independence in graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 397-409. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a14/

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