On General Position Sets in Cartesian Products

Identificadores
URI: http://hdl.handle.net/10498/26516
DOI: 10.1007/s00025-021-01438-x
ISSN: 1422-6383
ISSN: 1420-9012
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2021-08Department
MatemáticasSource
Results Math 76, 123 (2021)Abstract
The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gpsets of G. The general position number of cylinders Pr square Cs is deduced. It is proved that gp(Cr square C-s). {6, 7} whenever r >= s = 3, s >=not equal 4, and r >= 6. A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in Pr square Ps, where r, s >= 2, is also determined.
Subjects
General position problem; Cartesian product of graphs; paths and cycles; probabilistic constructions; exact enumerationCollections
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