Opuscula Mathematica
Opuscula Math. 29, no. 1 (), 5-14
Opuscula Mathematica

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

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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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