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	Volume 4, Issue 2 Pg 95 - 186 (October 2009)
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Advances and Applications in Discrete Mathematics

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.

Advances and Applications in Discrete Mathematics
Volume 4, Issue 2, Pages 169 - 186 (October 2009)

GRAPHS WITH METRIC DIMENSION TWO - A CHARACTERIZATION
G. Sudhakara (India) and A. R. Hemanth Kumar (India)

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

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.

Keywords and phrases: metric dimension, metric basis, distance partition.

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