Iswadi, Hazrul and Baskoro, Edy Tri and Salman, A.N.M and Simanjuntak, Rinovia (2010) The Metric Dimension of Amalgamation of Cycles. Far East Journal of Mathematical Sciences (FJMS), 41 (1). pp. 19-31. ISSN 0972-0871
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Abstract
For an ordered set W = {w_1, w_2 , ..., 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 ), ..., 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 voi called a terminal. The amalgamation Amal {Gi , 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Amalgamation, Cycles, Resolving set, Metric Dimension |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Academic Department > Department of Mathematics and Natural Science |
| Depositing User: | Hazrul Iswadi 6179 |
| Date Deposited: | 08 Mar 2012 07:03 |
| Last Modified: | 20 Mar 2012 01:43 |
| URI: | http://repository.ubaya.ac.id/id/eprint/172 |
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