Sudhakara, G and Kumar, Hemanth A R (2009) Graphs With Metric Dimension Two  A Characterization. Advances and Applications in Discrete Mathematics, 4 (2). pp. 169186. ISSN 09741658

PDF
SGpaper7.pdf  Published Version Download (5MB) 
Abstract
In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever We also find a bound for cardinality of any distance partite set with reference to a given vertex, whenever Also, in a graph G with a bound for cardinality of any distance partite set as well as a bound for number of vertices in any subgraph H of G is obtained in terms of diam H.
Item Type:  Article 

Subjects:  Engineering > MIT Manipal > Mathematics 
Depositing User:  MIT Library 
Date Deposited:  14 Mar 2013 06:53 
Last Modified:  14 Mar 2013 06:53 
URI:  http://eprints.manipal.edu/id/eprint/79039 
Actions (login required)
View Item 