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. 349364. ISSN 09757074

PDF
27Hemanth_Kumar467.pdf  Published Version Download (151kB) 
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 
Actions (login required)
View Item 