Dimensi Matriks Dan Dimensi Partisi Pada Graf Hasil Operasi Korona
Abstract
LetπΊ(π,πΈ)is a connected graph.For an ordered set π={π€1,π€2,β¦,π€π} of vertices, πβπ(πΊ), and a vertex π£βπ(πΊ), the representation of π£ with respect to π is the ordered k-tuple π(π£|π)={π(π£,π€1),π(π£,π€2),β¦,π(π£,π€π)|βπ£βπ(πΊ)}. 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 πΊ. The metric dimension of πΊ, denoted by πππ(πΊ), is the number of vertices in a basis of πΊ. Then, for a subset S of V(G), the distance between u and S is π(π£,π)=πππ{π(π£,π₯)|βπ₯βπ,βπ£βπ(πΊ)}. Let Ξ =(π1,π2,β¦,ππ)be an ordered l-partition of V(G), forβππβπ(πΊ) danπ£βπ(πΊ), the representation of v with respect to Ξ is the l-vector π(π£|Ξ )=(π(π£,π1),π(π£,π2),β¦,π(π£,ππ)). The set Ξ is called a resolving partition for G if the πβvector π(π£|Ξ ),βπ£βπ(πΊ)are distinct. The minimum l for which there is a resolving l-partition of V(G) is the partition dimension of G, denoted by ππ(πΊ). In this paper, we determine the metric dimension and the partition dimension of corona product graphs πΎπβ¨πΎπβ1, and we get some result that the metric dimension and partition dimension of πΎπβ¨πΎπβ1respectively isπ(πβ2) and 2πβ1, forπβ₯3.
Keyword: Metric dimention, partition dimenstion,corona product graphs