Pré-Publication, Document De Travail Année : 2024

The n/2-bound for locating-dominating sets in subcubic graphs

Résumé

The location-domination number is conjectured to be at most half of the order for twin-free graphs with no isolated vertices. We prove that this conjecture holds and is tight for subcubic graphs. We also show that the same upper bound holds for subcubic graphs with open twins of degree 3 and closed twins of any degree, but not for subcubic graphs with open twins of degree 1 or 2. These results then imply that the same upper bound holds for all cubic graphs (with or without twins) except $K_4$ and $K_{3,3}$.

Dates et versions

hal-05002806 , version 1 (24-03-2025)

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Dipayan Chakraborty, Anni Hakanen, Tuomo Lehtilä. The n/2-bound for locating-dominating sets in subcubic graphs. 2024. ⟨hal-05002806⟩
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