Dimensi Matriks Dan Dimensi Partisi Pada Graf Hasil Operasi Korona
| Main Author: | Listiana, Yuni |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | ind |
| Terbitan: |
Universitas Dr. Soetomo
, 2017
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| Subjects: | |
| Online Access: |
http://ejournal.unitomo.ac.id/index.php/mipa/article/view/235 http://ejournal.unitomo.ac.id/index.php/mipa/article/view/235/140 |
Daftar Isi:
- LetG(V,E)is a connected graph.For an ordered set W={w1,w2,...,wk} of vertices, W⊆V(G), and a vertex v∈V(G), the representation of v with respect to W is the ordered k-tuple r(v|W)={d(v,w1),d(v,w2),...,d(v,wk)|∀v∈V(G)}. The set W is called a resolving set of 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. Then, for a subset S of V(G), the distance between u and S is d(v,S)=min{d(v,x)|∀x∈S,∀v∈V(G)}. Let Π=(S1,S2,...,Sl)be an ordered l-partition of V(G), for∀Sl⊂V(G) danv∈V(G), the representation of v with respect to Π is the l-vector r(v|Π)=(d(v,S1),d(v,S2),...,d(v,Sl)). The set Π is called a resolving partition for G if the l−vector r(v|Π),∀v∈V(G)are distinct. The minimum l for which there is a resolving l-partition of V(G) is the partition dimension of G, denoted by pd(G). In this paper, we determine the metric dimension and the partition dimension of corona product graphs Kn⨀Kn−1, and we get some result that the metric dimension and partition dimension of Kn⨀Kn−1respectively isn(n−2) and 2n−1, forn≥3.Keyword: Metric dimention, partition dimenstion,corona product graphs