A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance}...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Shahrood University of Technology
2020-01-01
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| Series: | Journal of Algebraic Systems |
| Subjects: | |
| Online Access: | http://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf |
| Summary: | The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. <br /> Giving a characterization for those graphs whose metric dimensions are two, we enumerate the number of $n$ vertex metric two dimensional graphs with basic distance 1. |
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| ISSN: | 2345-5128 2345-511X |