On Locating-Dominating Set of Regular Graphs
Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8147514 |
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| _version_ | 1832560545115406336 |
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| author | Anuwar Kadir Abdul Gafur Suhadi Wido Saputro |
| author_facet | Anuwar Kadir Abdul Gafur Suhadi Wido Saputro |
| author_sort | Anuwar Kadir Abdul Gafur |
| collection | DOAJ |
| description | Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is called k-regular graph if every vertex of G is adjacent to k other vertices of G. In this paper, we determine the locating-dominating number of k-regular graph of order n, where k=n−2 or k=n−3. |
| format | Article |
| id | doaj-art-ac4695055d454d32a7e5bd39d90d5c4e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ac4695055d454d32a7e5bd39d90d5c4e2025-02-03T01:27:22ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/81475148147514On Locating-Dominating Set of Regular GraphsAnuwar Kadir Abdul Gafur0Suhadi Wido Saputro1Department of Mathematics, Pasific Morotai University, Morotai, IndonesiaDepartment of Mathematics, Bandung Institute of Technology, Bandung, IndonesiaLet G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is called k-regular graph if every vertex of G is adjacent to k other vertices of G. In this paper, we determine the locating-dominating number of k-regular graph of order n, where k=n−2 or k=n−3.http://dx.doi.org/10.1155/2021/8147514 |
| spellingShingle | Anuwar Kadir Abdul Gafur Suhadi Wido Saputro On Locating-Dominating Set of Regular Graphs Journal of Mathematics |
| title | On Locating-Dominating Set of Regular Graphs |
| title_full | On Locating-Dominating Set of Regular Graphs |
| title_fullStr | On Locating-Dominating Set of Regular Graphs |
| title_full_unstemmed | On Locating-Dominating Set of Regular Graphs |
| title_short | On Locating-Dominating Set of Regular Graphs |
| title_sort | on locating dominating set of regular graphs |
| url | http://dx.doi.org/10.1155/2021/8147514 |
| work_keys_str_mv | AT anuwarkadirabdulgafur onlocatingdominatingsetofregulargraphs AT suhadiwidosaputro onlocatingdominatingsetofregulargraphs |