A characterization of graphs with upper locating-domination number equal to $n-2$

Mimouni, Malika; Ouldrabah, Lyes; Ikhlef-Eschouf, Noureddine

doi:10.22108/toc.2025.139873.2128

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	A characterization of graphs with upper locating-domination number equal to $n-2$
Transactions on Combinatorics
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نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.139873.2128
نویسندگان
Malika Mimouni^* ¹؛ Lyes Ouldrabah²؛ Noureddine Ikhlef-Eschouf³
¹Laboratory, Department of Mathematics (LATSI), Faculty of Sciences, University of Blida 1, P.O.Box 270, Blida, Algeria
²Laboratory of Mathematics and its Applications (LMA), Faculty of Technology, Medea University, Medea, Algeria
³Laboratory of Mathematics and its Applications (LMA), Faculty of Sciences, Medea University, Medea, Algeria
چکیده
A set $D$ of vertices in a graph $G$ is called a dominating set of $G$ if every vertex in $V\left( G\right) \backslash D$ has at least one neighbor in $D$. A dominating set $D$ of $G$ is called a locating-dominating set of $G$ if every two vertices in $V\left( G\right) \backslash D$ have two distinct neighborhood sets. The upper locating-domination number $\Gamma_{L}(G)$ is the maximum cardinality of a minimal locating-dominating set of $G.$ In this paper, we characterize the graphs with $\Gamma_{L}\left( G\right) =n-2$.
کلیدواژه‌ها
dominating set؛ locating-dominating set؛ upper locating-domination number

مراجع
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A characterization of graphs with upper locating-domination number equal to $n-2$