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Vertices belonging to all or to no minimum locating dominating sets of trees

Blidia M., Lounes R.

Opuscula Mathematica

2009

Vol. 29, no. 1

5-14

A set D of vertices in a graph G is a locating-dominating set if for every two vertices u, v of G \ D the sets N(u) ∩ D and N (v) ∩ D are non-empty and different. In this paper, we characterize vertices that are in all or in no minimum locating dominating sets in trees. The characterization guarantees that the γL-excellent tree can be recognized in a polynomial time.