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description Journal article public Electronic Journal of Graph Theory and Applications

On Open Neighborhood Locating-dominating in Graphs

Mustapha Chellali, Nader Jafari Rad, Suk Jai Seo, Peter James Slater
Published 2014

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 (G) ≥ 2 that are C4-free with OLD(G) = n-1.

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  • visibility 210 views
  • get_app 114 downloads