On open neighborhood locating-dominating in graphs
| Main Authors: | Chellali, Mustapha; LAMDA-Laboratory, Department of Mathematics, University of Blida, Blida, Algeria, Rad, Nader Jafari; Department of Mathematics, Shahrood University of Technology, Shahrood, Iran, Seo, Suk Jai; Computer Science Department, Middle Tennessee State University, Murfreesboro, TN 37132, U.S.A, Slater, Peter James; Mathematical Sciences Department and Computer Science Department, University of Alabama in Huntsville, Huntsville, AL 35899 USA |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2014
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/63 http://www.ejgta.org/index.php/ejgta/article/view/63/20 |
Daftar Isi:
- 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.