Graphs with metric dimension two- A characterization

G. Sudhakara, A. R. Hemanth Kumar

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)622-627
Number of pages6
JournalWorld Academy of Science, Engineering and Technology
Volume36
Publication statusPublished - 01-12-2009

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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