On (<em>k</em>, <em>ℓ</em>)-locating colorings of graphs

Research Article

On (k, ℓ)-locating colorings of graphs

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 , 2024 , pages: 2163–2175
DOI: 10.2989/16073606.2024.2364301
Author(s): Michael A. Henning University of Johannesburg, South Africa , Mostafa Tavakoli Ferdowsi University of Mashhad, Iran
Keywords: Primary: 05C15 , Secondary: 05C69 , (k , ℓ)-locating coloring , locating coloring , neighbor-locating coloring , corona product , edge corona product , ILP model
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Abstract

Let c: V(G) → {1, . . . , ℓ} = [ℓ] be a proper vertex coloring of G and C(i) = {u ∈ V(G): c(u) = i} for i ∈ [ℓ]. The k-color code rk (v|c) of vertex v is the ordered ℓ-tuple (aG (v,C(1)), . . . , aG (v,C(ℓ))) where
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