Title : ( A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION )
Authors: mostafa mohagheghi nejhad , Freydoon Rahbarnia , Madjid Mirzavaziri , Reza Ghanbari ,
Full TextAbstract
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.
Keywords
Metric dimension; Resolving set; Metric basis; Basic distance; Contour of a graph
@article{paperid:1078196,
author = {Mohagheghi Nejhad, Mostafa and Rahbarnia, Freydoon and Madjid Mirzavaziri, and Ghanbari, Reza},
title = {A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION},
journal = {Journal of Algebraic Systems},
year = {2020},
volume = {7},
number = {2},
month = {January},
issn = {2345-5128},
pages = {179--187},
numpages = {8},
keywords = {Metric dimension; Resolving set; Metric basis; Basic distance; Contour of a graph},
}
%0 Journal Article
%T A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
%A Mohagheghi Nejhad, Mostafa
%A Rahbarnia, Freydoon
%A Madjid Mirzavaziri,
%A Ghanbari, Reza
%J Journal of Algebraic Systems
%@ 2345-5128
%D 2020
