Asmiati, Asmiati and Junaidi, Akmal
*Partition Dimension of Generalized Petersen Graphs Pn;k for
k = 1; 2.*
In: International Conference on Graph Theory and Information Security, 17-19 Juli 2019, Jember.
(Unpublished)

## Abstract

The partition dimension was firstly studied by Chartrand et al. in [1] [2]. Let G = (V;E) be a finite, simple, and connected graph. For an ordered k-partition � = fS1; S2; :::; Skg of V (G) and a vertex v 2 V (G), the representation of v with respect to � is defined as the k-vector r(vj�) = (d(v; S1); d(v; S2); :::; d(v; Sk)). The partition � is called a resolving partition if the k-vectors r(vj�); v 2 V (G) are distinct. The minimum k for which there is a resolving k-partition of V (G) is the partition dimension of G, denoted by pd(G). The generalized Petersen graph P(n;m), n � 3 and 1 � m � d(n

Item Type: | Conference or Workshop Item (Speech) |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika |

Depositing User: | ASMIATI |

Date Deposited: | 29 Oct 2019 02:51 |

Last Modified: | 29 Oct 2019 02:51 |

URI: | http://repository.lppm.unila.ac.id/id/eprint/14635 |

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