NONLOCAL METRIC DIMENSION: AN IMPROVEMENT FOR BOUNDS

Let G be a connected graph. The nonlocal metric dimension of G, denoted by dimne (G), is introduced as the cardinality of a smallest nonlocal resolving set, i.e. a set of vertices that resolves every pair of non-adjacent vertices of G. Klavžar and Kuziak [Nonlocal Metric Dimension of Graphs, Bull. Malays. Math. Sci. Soc. (۲۰۲۳) ۴۶-۶۶] introduced this concept and gave some bounds on it. The purpose of this paper is to improve the bounds and conditions. ۲۰۲۰ Mathematics Subject Classification. ۰۵C۱۵. Key words and phrases. Nonlocal metric dimension, resolving set, girth, edge cover.

کلیدواژه ها:

Nonlocal metric dimension ، resolving set ، girth ، edge cover