Distance-k Domination Number in Triangular Matchstick Graphs and Triangulated Rectangular Grids - Gutierrez, Juan; Neira, Jorge (Anais do Encontro de Teoria da Computação (ETC), 2026)
A distance-k dominating set of a graph is a set of vertices such that every vertex lies within distance k of some vertex in the set; its minimum size is the distance-k domination number γ k . We study γ k for triangular matchstick graphs and triangulated rectangular grids. For triangulated rectangular grids, we give upper bounds for γ and γ 2 . For triangular matchstick graphs T d , we correct two upper-bound statements of Harris et al. [Harris et al. 2020], improve the bound for k = 1, derive an upper bound for k = 2 and relate γ k to the radius of T d .