NDLI: Metric Dimension Threshold of Graphs

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Author	Meysam Korivand Kazem Khashyarmanesh Mostafa Tavakoli
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 du,w≠dv,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 dimthG. 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.
Related Links	http://dx.doi.org/10.1155/2022/1838719
e-ISSN	23144785
DOI	10.1155/2022/1838719
Journal	Journal of Mathematics
Volume Number	2022
Language	English
Publisher	Hindawi Limited
Publisher Date	2022-01-01
Publisher Place	United Kingdom
Access Restriction	Open
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article

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