@article{(Open Science Index):https://publications.waset.org/pdf/13897, title = {Graphs with Metric Dimension Two-A Characterization}, author = {Sudhakara G and Hemanth Kumar A.R}, country = {}, institution = {}, 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 (i.e. β (G) = 2 ) 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 β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H . }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {3}, number = {12}, year = {2009}, pages = {1128 - 1133}, ee = {https://publications.waset.org/pdf/13897}, url = {https://publications.waset.org/vol/36}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 36, 2009}, }