Asmiati, Asmiati and Yulianti, Lyra and Aristoteles, Aristoteles
(2019)
*Characterizing Generalized Petersen Graphs
with Locating Chromatic Number Five.*
In: International Conference on Mathematics and Mathematics Education, 3-4 Agustus 2019, UNP, Padang.
(Unpublished)

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## Abstract

Consider as the given connected graph and as the proper coloring of using k colors for some positive integer k. We denote as the partition of , where C_i is the color class, the set of vertices that given the i-th color, for . For an arbitrary vertex v V(G), the color code is defined as the ordered -tuple c_π (v)=(d(v,C_1 ),d(v,C_2 ),…,d(v,C_k )), where for . If for every two vertices u,v V(G), their color codes are different, c_π (u)≠ c_π (v), then c is defined as the locating coloring of using k colors. The locating chromatic number of G, denoted by χ_L (G), is the minimum k such that G has a locating coloring. The generalized Petersen Graph P_(n,k),n≥3, 1≤k≤⌈(n-1)/2⌉, consists of an outer n-cycle u_1, u_2,…,u_n, a set n spokes u_i v_(i,) 1≤i≤n, and n edges v_i v_(i+k) , with indices taken modulo n. In this paper, we characterize generalized Petersen graphs whose locating-chromatic number is 5.

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/14659 |

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