Metric Dimension Threshold of Graphs
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 dimensi...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1838719 |
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| author | Meysam Korivand Kazem Khashyarmanesh Mostafa Tavakoli |
| author_facet | Meysam Korivand Kazem Khashyarmanesh Mostafa Tavakoli |
| author_sort | Meysam Korivand |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-61fb12aee746449580fce5b4e5f14de5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-61fb12aee746449580fce5b4e5f14de52025-02-03T06:00:56ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1838719Metric Dimension Threshold of GraphsMeysam Korivand0Kazem Khashyarmanesh1Mostafa Tavakoli2Department of Pure MathematicsDepartment of Pure MathematicsDepartment of Applied MathematicsLet 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.http://dx.doi.org/10.1155/2022/1838719 |
| spellingShingle | Meysam Korivand Kazem Khashyarmanesh Mostafa Tavakoli Metric Dimension Threshold of Graphs Journal of Mathematics |
| title | Metric Dimension Threshold of Graphs |
| title_full | Metric Dimension Threshold of Graphs |
| title_fullStr | Metric Dimension Threshold of Graphs |
| title_full_unstemmed | Metric Dimension Threshold of Graphs |
| title_short | Metric Dimension Threshold of Graphs |
| title_sort | metric dimension threshold of graphs |
| url | http://dx.doi.org/10.1155/2022/1838719 |
| work_keys_str_mv | AT meysamkorivand metricdimensionthresholdofgraphs AT kazemkhashyarmanesh metricdimensionthresholdofgraphs AT mostafatavakoli metricdimensionthresholdofgraphs |