Title of article :
On open neighborhood locating-dominating in graphs
Author/Authors :
Chellali, Mustapha University of Blida - Department of Mathematics, LAMDA-Laboratory, Algeria , Jafari Rad, Nader shahrood university of technology - Department of Mathematics, شاهرود, ايران , Seo, Suk J. Middle Tennessee State University - Computer Science Department, U.S.A , Slater, Peter J. University of Alabama in Huntsville - Mathematical Sciences Department, Computer Science Department, USA
Abstract :
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 δ(G) ≥ 2 that are C4-free with OLD(G) = n − 1.
Keywords :
domination , open neighborhood locating , dominating
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
