Characterization of classes of graphs with large general position number

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 of G. The graphs G of order n with were already characterized. In this paper, we characterize the classes of all connected graphs of order with the general position number

Keywords

• diameter
• girth
• general position set
• general position number