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.
Mohagheghy Nezhad, M., Rahbarnia, F., Mirzavaziri, M., Ghanbari, R. (2020). A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION. Journal of Algebraic Systems, 7(2), 179-187. doi: 10.22044/jas.2019.7367.1363
MLA
M. Mohagheghy Nezhad; F. Rahbarnia; M. Mirzavaziri; R. Ghanbari. "A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION". Journal of Algebraic Systems, 7, 2, 2020, 179-187. doi: 10.22044/jas.2019.7367.1363
HARVARD
Mohagheghy Nezhad, M., Rahbarnia, F., Mirzavaziri, M., Ghanbari, R. (2020). 'A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION', Journal of Algebraic Systems, 7(2), pp. 179-187. doi: 10.22044/jas.2019.7367.1363
VANCOUVER
Mohagheghy Nezhad, M., Rahbarnia, F., Mirzavaziri, M., Ghanbari, R. A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION. Journal of Algebraic Systems, 2020; 7(2): 179-187. doi: 10.22044/jas.2019.7367.1363
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