## 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 language | English |
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Pages (from-to) | 181-196 |

Number of pages | 16 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 66 |

Issue number | 2 |

Publication status | Published - Jul 2012 |

## Keywords

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