@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},
	}