Iswadi, Hazrul
(2011)
*Batas Atas Bilangan Dominasi Lokasi Metrik Graf Hasil Operasi Korona.*
Prosiding Seminar Nasional Teknologi Informasi dan Multimedia 2011 (SNASTIA 2011).
pp. 1-5.
ISSN 1979-3960

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## Abstract

For an ordered set W = {w_1, w_2 , ..., w_k } of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v |W) = (d(v,w_1), d(v,w_2 ), ..., d (v,w_k )), where d(x,y) represents the distance between the vertices x and y. The set W is called a locating set for G if every vertex of G has a distinct representation. A locating set containing a minimum number of vertices is called a basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A set W of vertices of a connected graph G is a dominating set of G if every vertex in V – W is adjacent to a vertex of W. A dominating set W in a connected graph G is a metric-locating-dominating set, or an MLD-set, if W is both a dominating set and a locating set in G. The metric-location-domination number \gamma_M(G) of G is the minimum cardinality of an MLD-set in G. A graph G corona H, G \odot H, is defined as a graph which formed by taking n copies of graphs H_1, H_2, …, H_n of H and connecting i-th vertex of G to every vertices of Hi. We determine the upper bound of the metric-location-domination number of corona product graphs in terms of the metric dimension of G or H.

Item Type: | Article |
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Uncontrolled Keywords: | resolving set, dominating set, metric dimension, metric-location-domination number, corona |

Subjects: | Q Science > QA Mathematics |

Divisions: | Academic Department > Department of Mathematics and Natural Science |

Depositing User: | Hazrul Iswadi 6179 |

Date Deposited: | 29 Mar 2012 05:37 |

Last Modified: | 24 Mar 2021 14:17 |

URI: | http://repository.ubaya.ac.id/id/eprint/272 |

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