On Open Neighborhood Locating-dominating in Graphs

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

Abstrak

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.

Metrics

  • 70 kali dilihat
  • 52 kali diunduh

Jurnal

Electronic Journal of Graph Theory and Applications

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to ... tampilkan semua