Journal of Prime Research in Mathematics
Vol. 1 (2010), Issue 1, pp. 22 – 31
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
Graphs with same diameter and metric dimension
Imrana Kousar
Department of Mathematics, National University of Computer and Emerging Sciences(Fast), Lahore, Pakistan.
Ioan Tomescu
Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 010014 Bucharest, Romania.
Syed Muhammad Husnine
Department of Mathematics, National University of Computer and Emerging Sciences(Fast), Lahore, Pakistan.
\(^{1}\)Corresponding Author: imrana.kousar@hotmail.com
Copyright © 2010 Imrana Kousar, Ioan Tomescu, Syed Muhammad Husnine. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2010.
Abstract
The cardinality of a metric basis of a connected graph \(G\) is called its metric dimension, denoted by \(dim(G)\) and the maximum value of distance between vertices of \(G\) is called its diameter. In this paper, the graphs \(G\) with diameter 2 are characterized when \(dim(G) = 2.\)
Keywords:
Distance, eccentricity, diameter, basis, metric dimension.