Opuscula Math. 29, no. 1 (2009), 5-14
http://dx.doi.org/10.7494/OpMath.2009.29.1.5

Opuscula Mathematica

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

Mostafa Blidia
Rahma Lounes

Abstract. A set $$D$$ of vertices in a graph $$G$$ is a locating-dominating set if for every two vertices $$u$$, $$v$$ of $$G \setminus D$$ the sets $$N(u) \cap D$$ and $$N(v) \cap D$$ 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 $$\gamma_L$$-excellent tree can be recognized in a polynomial time.

Keywords: domination, locating domination.

Mathematics Subject Classification: 05C69.

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• Mostafa Blidia
• University of Blida, LAMDA-RO, Department of Mathematics, B.P. 270, Blida, Algeria
• Rahma Lounes
• University of Blida, LAMDA-RO, Department of Mathematics, B.P. 270, Blida, Algeria
• Received: 2007-02-10.
• Revised: 2009-05-02.
• Accepted: 2009-05-11.

Cite this article as:
Mostafa Blidia, Rahma Lounes, Vertices belonging to all or to no minimum locating dominating sets of trees, Opuscula Math. 29, no. 1 (2009), 5-14, http://dx.doi.org/10.7494/OpMath.2009.29.1.5

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