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Publication# Sphere-of-Influence Graphs in Normed Spaces

Abstract

We showthat any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than 5dk, thus obtaining a common generalization of results of Furedi and Loeb (Proc AmMath Soc 121(4): 1063-1073, 1994 [1]) and Guibas et al. (Sphere-of-influence graphs in higher dimensions, Intuitive geometry [Szeged, 1991], 1994, pp. 131-137 [2]).

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Related concepts (1)

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.