Metric Dimension Threshold of Graphs. (14th September 2022)

• Record Type: Journal Article
• Authors: Korivand, Meysam; Khashyarmanesh, Kazem; Tavakoli, Mostafa
• Other Names: Farshadifar Faranak Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-09-14
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/1838719
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : Let G be a connected graph. A subset S of vertices of G is said to be a resolving set of G, if for any two vertices u and v of G there is at least a member w of S such that d u, w ≠ d v, w . The minimum number t that any subset S of vertices G with S = t is a resolving set for G, is called the metric dimension threshold, and is denoted by dim th G . In this paper, the concept of metric dimension threshold is introduced according to its application in some real-word problems. Also, the metric dimension threshold of some families of graphs and a characterization of graphs G of order n for which the metric dimension threshold equals 2, n − 2, and n − 1 are given. Moreover, some graphs with equal the metric dimension threshold and the standard metric dimension of graphs are presented.