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Graphs with metric dimension two -- a characterization (2009).
| Content Provider | CiteSeerX |
|---|---|
| Author | Sudhakara, G. Hemanth Kumar A., R. |
| 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. |
| File Format | |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Content Type | Text |
