# Graphs with metric dimension two- A characterization

G. Sudhakara, A. R. Hemanth Kumar

Research output: Contribution to journalArticle

4 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 language English 622-627 6 World Academy of Science, Engineering and Technology 36 Published - 01-12-2009

Polynomials

### All Science Journal Classification (ASJC) codes

• Engineering(all)

### Cite this

title = "Graphs with metric dimension two- A characterization",
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.",
author = "G. Sudhakara and {Hemanth Kumar}, {A. R.}",
year = "2009",
month = "12",
day = "1",
language = "English",
volume = "36",
pages = "622--627",
journal = "World Academy of Science, Engineering and Technology",
issn = "2010-376X",
publisher = "World Academy of Science Engineering and Technology",

}

Graphs with metric dimension two- A characterization. / Sudhakara, G.; Hemanth Kumar, A. R.

In: World Academy of Science, Engineering and Technology, Vol. 36, 01.12.2009, p. 622-627.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Graphs with metric dimension two- A characterization

AU - Sudhakara, G.

AU - Hemanth Kumar, A. R.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

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