Graphs With Metric Dimension Two - A Characterization

Sudhakara, G and Kumar, Hemanth A R (2009) Graphs With Metric Dimension Two - A Characterization. Advances and Applications in Discrete Mathematics, 4 (2). pp. 169-186. ISSN 0974-1658

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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

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