An upper bound on average touching number of a Voronoi partition (Q1262313)

A Voronoi partition is defined by the configurations of N centerpoints in n dimensional Euclidean space. The total number of nearest neighbor points for a given centerpoint in the partition is called its touching number. It is shown that the average touching number of all points in Voronoi partition is not greater than the n dimensional kissing number which is the maximum number of unit spheres that can touch a given unit sphere without overlapping. The Voronoi partition in packing and covering has applications in computer science, physics, chemistry and other field.