Iswadi, Hazrul and Baskoro, Edy Tri and Simanjuntak, Rinovia (2011) On the Metric Dimension of Corona Product of Graphs. Far East Journal of Mathematical Sciences (FJMS), 52 (2). pp. 155-170. 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 metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A graph G corona H, G ⊙ H, is de�fined as a graph which formed by taking n copies of graphs H_1,H_2,...,H_n of H and connecting i-th vertex of G to the vertices of H_i. In this paper, we determine the metric dimension of corona product graphs G⊙H, the lower bound of the metric dimension of K_1 +H and determine some exact values of the metric dimension of G⊙H for some particular graphs H.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Corona graph, metric dimension, resolving set |
| 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 01:45 |
| URI: | http://repository.ubaya.ac.id/id/eprint/174 |
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