Author

A. C. Gomes

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Preprint Aug 2026

Optimal and quasi-optimal locating-dominating densities in the infinite hexagonal grid with a finite number of rows

A set of vertices $S$ of a graph $G$ is locating-dominating if $S$ is dominating and, for each pair of distinct vertices not in $S$, their neighborhoods in $S$ are distinct. We present results on the minimum density of such sets in the infinite hexagonal grid with a finite number of rows $k$, also known as the hexagona...

A. C. Gomes, Y. Wakabayashi · 1 citation

Preprint Aug 2026

The complexity of minimum-density locating-dominating set in infinite periodic graphs

It is proved that the minimum-density LDS problem in infinite $\mathbb{Z}$-periodic graphs with a finite period is NP-hard, which bridges the gap between cardinality minimization on finite graphs and density minimization on infinite graphs via a rigorous periodic reduction.

A. C. Gomes, Y. Wakabayashi · 1 citation