We consider an extension of the triangular-distance Delaunay graphs
(TD-Delaunay) on a set P of points in the plane. In TD-Delaunay, the convex
distance is defined by a fixed-oriented equilateral triangle â–½,
and there is an edge between two points in P if and only if there is an empty
homothet of â–½ having the two points on its boundary. We consider
higher-order triangular-distance Delaunay graphs, namely k-TD, which contains
an edge between two points if the interior of the homothet of â–½
having the two points on its boundary contains at most k points of P. We
consider the connectivity, Hamiltonicity and perfect-matching admissibility of
k-TD. Finally we consider the problem of blocking the edges of k-TD.Comment: 20 page