On open neighborhood locating-dominating in graphs
<p>A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The open neighborhood locating-dominating number OLD(G) is the minimum cardina...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2014-10-01
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| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/63 |
| _version_ | 1818217406745542656 |
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| author | Mustapha Chellali Nader Jafari Rad Suk Jai Seo Peter James Slater |
| author_facet | Mustapha Chellali Nader Jafari Rad Suk Jai Seo Peter James Slater |
| author_sort | Mustapha Chellali |
| collection | DOAJ |
| description | <p>A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The open neighborhood locating-dominating number OLD(G) is the minimum cardinality of an OLD-set for G. In this paper we characterize graphs G of order n with OLD(G) = 2, 3, or n and graphs with minimum degree (G) ≥ 2 that are C4-free with OLD(G) = n-1.</p> |
| first_indexed | 2024-12-12T07:07:22Z |
| format | Article |
| id | doaj.art-f1a89f4f715f43e9b1d27482cca64dc5 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-12-12T07:07:22Z |
| publishDate | 2014-10-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-f1a89f4f715f43e9b1d27482cca64dc52022-12-22T00:33:42ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872014-10-0122879810.5614/ejgta.2014.2.2.121On open neighborhood locating-dominating in graphsMustapha Chellali0Nader Jafari Rad1Suk Jai Seo2Peter James Slater3LAMDA-Laboratory, Department of Mathematics, University of Blida, Blida, AlgeriaDepartment of Mathematics, Shahrood University of Technology, Shahrood, IranComputer Science Department, Middle Tennessee State University, Murfreesboro, TN 37132, U.S.AMathematical Sciences Department and Computer Science Department, University of Alabama in Huntsville, Huntsville, AL 35899 USA<p>A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The open neighborhood locating-dominating number OLD(G) is the minimum cardinality of an OLD-set for G. In this paper we characterize graphs G of order n with OLD(G) = 2, 3, or n and graphs with minimum degree (G) ≥ 2 that are C4-free with OLD(G) = n-1.</p>https://www.ejgta.org/index.php/ejgta/article/view/63dominationopen neighborhood locating-dominating |
| spellingShingle | Mustapha Chellali Nader Jafari Rad Suk Jai Seo Peter James Slater On open neighborhood locating-dominating in graphs Electronic Journal of Graph Theory and Applications domination open neighborhood locating-dominating |
| title | On open neighborhood locating-dominating in graphs |
| title_full | On open neighborhood locating-dominating in graphs |
| title_fullStr | On open neighborhood locating-dominating in graphs |
| title_full_unstemmed | On open neighborhood locating-dominating in graphs |
| title_short | On open neighborhood locating-dominating in graphs |
| title_sort | on open neighborhood locating dominating in graphs |
| topic | domination open neighborhood locating-dominating |
| url | https://www.ejgta.org/index.php/ejgta/article/view/63 |
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