HigherOrder TriangularDistance Delaunay Graphs: GraphTheoretical Properties
Abstract
We consider an extension of the triangulardistance Delaunay graphs (TDDelaunay) on a set $P$ of points in the plane. In TDDelaunay, the convex distance is defined by a fixedoriented equilateral triangle $\triangledown$, and there is an edge between two points in $P$ if and only if there is an empty homothet of $\triangledown$ having the two points on its boundary. We consider higherorder triangulardistance Delaunay graphs, namely $k$TD, which contains an edge between two points if the interior of the homothet of $\triangledown$ having the two points on its boundary contains at most $k$ points of $P$. We consider the connectivity, Hamiltonicity and perfectmatching admissibility of $k$TD. Finally we consider the problem of blocking the edges of $k$TD.
 Publication:

arXiv eprints
 Pub Date:
 September 2014
 arXiv:
 arXiv:1409.5466
 Bibcode:
 2014arXiv1409.5466B
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 20 pages