TY - JOUR
ID - 1588
TI - A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Mohagheghy Nezhad, M.
AU - Rahbarnia, F.
AU - Mirzavaziri, M.
AU - Ghanbari, R.
AD - Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box
1159, Mashhad, Iran.
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad, Iran.
Y1 - 2020
PY - 2020
VL - 7
IS - 2
SP - 179
EP - 187
KW - Metric dimension
KW - Resolving set
KW - Metric basis
KW - Basic distance
KW - Contour of a graph
DO - 10.22044/jas.2019.7367.1363
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_1588.html
L1 - https://jas.shahroodut.ac.ir/article_1588_14ce71a7aec0d0417b21b3acf6be72d4.pdf
ER -