Sooryanrayana, B and Kumar, Hemanth and Sathyanarayana, B and Sudhakara, G and Subbareddy , NV (2011) Cluster Dimension of a Network. International Journal of Multidisciplinary Research and Advances in Engineering (IJMRAE), 3 (4). pp. 349-364. ISSN 0975-7074

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Abstract

We define the Cluster Dimension of a network is the minimum cardinality of a subset S of the set of nodes having the property that for any two distinct nodes x and y, there exist the node s1, s2 (need not be distinct) in S such that | ( , 1) ( , 1) | 1 d x s - d y s ³ and d(x, s2) < d(x, s) for all sÎS -{s2}. In this paper, we obtain sufficient conditions for a graph of cluster dimension n and a tight upper bound for the number of nodes of a network with prescribed dimension in terms of diameter. Also give an algorithm to determine cluster basis and dimensions of a given graph to show the NP completeness.

Item Type:	Article
Uncontrolled Keywords:	Metric dimension, metric basis, cluster dimension, cluster basis
Subjects:	Engineering > MIT Manipal > Computer Science and Engineering
Depositing User:	MIT Library
Date Deposited:	08 Nov 2011 10:50
Last Modified:	08 Nov 2011 10:50
URI:	http://eprints.manipal.edu/id/eprint/1449

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