%0 Journal Article
%T A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Mohagheghy Nezhad, M.
%A Rahbarnia, F.
%A Mirzavaziri, M.
%A Ghanbari, R.
%D 2020
%\ 01/01/2020
%V 7
%N 2
%P 179-187
%! A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
%K Metric dimension
%K Resolving set
%K Metric basis
%K Basic distance
%K Contour of a graph
%R 10.22044/jas.2019.7367.1363
%X 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.
%U https://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf