RT journal article
T1 General d-position sets
A1 Klavžar, Sandi
A1 Rall, Douglas F.
A1 González Yero, Ismael
A2 Matemáticas
K1 General d-position sets
K1 dissociation sets
K1 strong resolving graphs
K1 computational complexity
K1 infinite graphs
AB 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 cycle is computed and a structural characterization of general d-position sets is shown. Moreover, we present some relationships with other topics including strong resolving graphs and dissociation sets. We finish our exposition by proving that gp(d)(G) is infinite whenever G is an infinite graph and d is a finite integer.
PB UP FAMNIT
SN 1855-3966
YR 2021
FD 2021
LK http://hdl.handle.net/10498/26132
UL http://hdl.handle.net/10498/26132
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 13-nov-2026