Characterization of classes of graphs with large general position number. Issue 3 (1st September 2020)

• Record Type: Journal Article
• Authors: Thomas, Elias John; Chandran S. V., Ullas
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 17:Issue 3(2020)
• Page Start: 935
• Page End: 939
• Publication Date: 2020-09-01
• Subjects: Diameter -- girth -- general position set -- general position number; 05C12 -- 05C69
• DOI: 10.1016/j.akcej.2019.08.008
• Languages: English
• ISSNs: 0972-8600

Abstract

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.