The Metric Dimension of Graph with Pendant Edges
| Main Authors: | Iswadi, Hazrul, Baskoro, Edy Tri, Simanjuntak, Rinovia, Salman, A.N.M |
|---|---|
| Format: | Article PeerReviewed application/pdf |
| Terbitan: |
Charles Babbage Research Center
, 2008
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| Subjects: | |
| Online Access: |
http://repository.ubaya.ac.id/171/1/hazrul_The%20Metric%20Dimension%20of%20Graph%20with%20Pendant%20Edges_2008.pdf http://repository.ubaya.ac.id/171/ |
Daftar Isi:
- 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 two vertices of G have distinct representations. 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. In this paper, we determine the dimensions of some corona graphs G⊙K_1, and G⊙K_m for any graph G and m ≥ 2, and a graph with pendant edges more general than corona graphs G⊙K_m.