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Article . 2010
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The Metric Dimension of Amalgamation of Cycles

The metric dimension of amalgamation of cycles
Authors: Iswadi, Hazrul; Baskoro, Edy Tri; Salman, A.N.M; Simanjuntak, Rinovia;

The Metric Dimension of Amalgamation of Cycles

Abstract

Summary: For an ordered set \(W = \{w_1, w_2, \dots, w_k\}\) of vertices and a vertex \(v\) in a connected graph \(G\), the representation of \(v\) with respect to \(W\) is the ordered \(k\)-tuple \(r(v|W) = (d(v,w_1), d(v,w_2), \dots, d(v,w_k))\) where \(d(x,y)\) represents the distance between the vertices \(x\) and \(y\). The set \(W\) is called a resolving set for \(G\) if every vertex of \(G\) has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for \(G\). The dimension of \(G\), denoted by dim\((G)\) is the number of vertices in a basis of \(G\). Let \(\{G_i\}\) be a finite collection of graphs and each \(G_i\) has a fixed vertex \(v_{oi}\) called a terminal. The amalgamation Amal \(\{G_i, v_{oi}\}\) is formed by taking all of the \(G_i\) 's and identifying their terminals. In this paper, we determine the metric dimension of amalgamation of cycles.

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Keywords

Distance in graphs, basis, amalgamation, Graph operations (line graphs, products, etc.), resolving set, QA Mathematics, Paths and cycles, metric dimension

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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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