Journal of Algebraic Systems, Volume (7), No (2), Year (2020-1) , Pages (179-187)

Title : ( A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION )

Authors: mostafa mohagheghi nejhad , Freydoon Rahbarnia , Madjid Mirzavaziri , Reza Ghanbari ,

Citation: BibTeX | EndNote

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.

Keywords

Metric dimension; Resolving set; Metric basis; Basic distance; Contour of a graph
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@article{paperid:1078196,
author = {Mohagheghi Nejhad, Mostafa and Rahbarnia, Freydoon and Mirzavaziri, Madjid 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},
}

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%0 Journal Article
%T A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
%A Mohagheghi Nejhad, Mostafa
%A Rahbarnia, Freydoon
%A Mirzavaziri, Madjid
%A Ghanbari, Reza
%J Journal of Algebraic Systems
%@ 2345-5128
%D 2020

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