The partition dimension of the corona product of two graphs

Edy Tri Baskoro, Darmaji

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Let G(V, E) be a connected graph. For a vertex v ∈ V(G) and a subset S of V(G), the distance d(v, S) from v to S is min{d(v, w){pipe} w ∈ S}. For an ordered k-partition Π = {S 1, S 2,..., S k} of V(G), the representation of v with respect to Π is r(v {pipe} Π) = (d(v, S 1), d(v, S 2),..., d(v, S k)). The k-partition Π is called a resolving partition of G if all r(v {pipe} Π) for all v ∈V(G) are distinct. The partition dimension of a graph G is the smallest k such that G has a resolving k-partition. In this paper, we derive an upper bound of the partition dimension of the corona product G ⊙ H, where G, H are connected graphs and the diameter of H is at most 2. Furthermore, we also determine the exact value of the partition dimension of this corona product if G is either a path or a complete graph and H is a complete graph.

Original languageEnglish
Pages (from-to)181-196
Number of pages16
JournalFar East Journal of Mathematical Sciences
Volume66
Issue number2
Publication statusPublished - Jul 2012

Keywords

  • Complete graph
  • Corona product
  • Partition dimension
  • Path
  • Resolving partition

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