Cluster Dimension Two – A Characterization

Kumar, Hemanth A R and Sudhakara, G and Satyanarayana, B S (2011) Cluster Dimension Two – A Characterization. Global Journal of Mathematical Sciences : Theory and Practical, 3 (4). pp. 383-403. ISSN 0971-3200

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Abstract

In this paper, we define distance partition of a vertex set of a graph G with reference to a vertex set in it and with the help of the same a graph dimension two with cluster (I,e, βc(G)=2) is characterized. In this process, we develop a polynomial time algorithm that verifies if the cluster dimension of a given graph G is two. The same algorithm explores all the cluster bases of graph G whenever βc(G)=2. We also find bound for cardinality of any distance partite set with reference to a given vertex , whenever βc(G)=2. Also, in a graph G with βc(G)=2, a bound for cardinality of any distance partite set as well as a bound for number of vertices in any subgraph H of G is obtained in terms of diam H.

Item Type: Article
Uncontrolled Keywords: Cluster Dimension, Cluster basis, Distance Partition, Distance partite Set, Resolving Set, Metric Dimension, Metric basis,Strongly resolving set.
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 08 Jun 2013 09:07
Last Modified: 08 Jun 2013 09:07
URI: http://eprints.manipal.edu/id/eprint/136263

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