Abstract:The general d-position number gp d (G) of a graph G is the cardinality of a largest set S for which no three distinct vertices from S lie on a common geodesic of length at most d. This new graph parameter generalizes the well studied general position number. We first give some results concerning the monotonic behavior of gp d (G) with respect to the suitable values of d. We show that the decision problem concerning finding gp d (G) is NP-complete for any value of d. The value of gp d (G) when G is a path or a … Show more
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