Characterization of classes of graphs with large general position number. Issue 3 (1st September 2020) - Thomas, Elias John; Chandran S. V., Ullas
Abstract: Getting inspired by the famous no-three-in-line problem and by the general position subset selection problem from discrete geometry, the same is introduced into graph theory as follows. A set S of vertices in a graph G is a general position set if no element of S lies on a geodesic between any two other elements of S . The cardinality of a largest general position set is the general position number gp ( G ) of G . The graphs G of order n with gp ( G ) ∈ { 2, n, n − 1 } were already characterized. In this paper, we characterize the classes of all connected graphs of order n ≥ 4 with the general position number n − 2.