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Distance independence in graphs

J. Louis Sewell; Peter J. Slater — 2011

Discussiones Mathematicae Graph Theory

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 $β_{O D D} (G)$ where ODD = 1,3,5,....

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