Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4

Metric dimension Related Publications

4 Metric Dimension on Line Graph of Honeycomb Networks

Authors: M. Hussain, Aqsa Farooq

Abstract:

Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.

Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph

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3 Development of a Clustered Network based on Unique Hop ID

Authors: Sudhakar G, Hemanth Kumar, A. R., Satyanarayana B. S.

Abstract:

In this paper, Land Marks for Unique Addressing( LMUA) algorithm is develped to generate unique ID for each and every node which leads to the formation of overlapping/Non overlapping clusters based on unique ID. To overcome the draw back of the developed LMUA algorithm, the concept of clustering is introduced. Based on the clustering concept a Land Marks for Unique Addressing and Clustering(LMUAC) Algorithm is developed to construct strictly non-overlapping clusters and classify those nodes in to Cluster Heads, Member Nodes, Gate way nodes and generating the Hierarchical code for the cluster heads to operate in the level one hierarchy for wireless communication switching. The expansion of the existing network can be performed or not without modifying the cost of adding the clusterhead is shown. The developed algorithm shows one way of efficiently constructing the

Keywords: Metric dimension, Cluster dimension, Cluster Basis, Metric Basis

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2 Routing Algorithm for a Clustered Network

Authors: Hemanth KumarA.R, Sudhakara G., Satyanarayana B.S.

Abstract:

The Cluster Dimension of a network is defined as, which 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 Si, s2 (need not be distinct) in S such that ld(x,s1) — d(y, s1)1 > 1 and d(x,s2) < d(x,$) for all s E S — {s2}. In this paper, strictly non overlap¬ping clusters are constructed. The concept of LandMarks for Unique Addressing and Clustering (LMUAC) routing scheme is developed. With the help of LMUAC routing scheme, It is shown that path length (upper bound)PLN,d < PLD, Maximum memory space requirement for the networkMSLmuAc(Az) < MSEmuAc < MSH3L < MSric and Maximum Link utilization factor MLLMUAC(i=3) < MLLMUAC(z03) < M Lc

Keywords: Cluster, Metric dimension, Cluster dimension

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1 Graphs with Metric Dimension Two-A Characterization

Authors: Sudhakara G, Hemanth Kumar A.R

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 .

Keywords: Metric dimension, Metric Basis, Distance partition

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