@article {
author = {Mohagheghy Nezhad, M. and Rahbarnia, F. and Mirzavaziri, M. and Ghanbari, R.},
title = {A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION},
journal = {Journal of Algebraic Systems},
volume = {7},
number = {2},
pages = {179-187},
year = {2020},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2019.7367.1363},
abstract = {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 $B$. 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.},
keywords = {Metric dimension,Resolving set,Metric basis,Basic distance,Contour of a graph},
url = {https://jas.shahroodut.ac.ir/article_1588.html},
eprint = {https://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf}
}