A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
نویسندگان
1 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
2 Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
3 Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
4 Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
doi
10.22044/jas.2019.7367.1363چکیده
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.
