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
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
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
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
A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
1Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
2Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
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.
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