Relative neighborhood graph
- Relative neighborhood graph
In computational geometry, the relative neighborhood graph (RNG) was proposed by Godfried Toussaint in 1980. [G. T. Toussaint, “The relative neighborhood graph of a finite planar set,” Pattern Recognition, vol. 12, pp. 261-268, 1980.] There has been a lot of research on this kind of graph. [ [http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=163414 Welcome to IEEE Xplore 2.0: Relative neighborhood graphs and their relatives ] ] [ [http://portal.acm.org/citation.cfm?id=322386 The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees ] ]
Definition
The relative neighborhood graph of a graph "G" = ("V", "E"), denoted by RNG("G"), is the set of all edges "uv" є "E" such that there is no vertex or point "w" where "uw" є "E", "wv" є "E" and ||"uw"|| < ||"uv"|| and ||"wv"|| < ||"uv"||.
References
Wikimedia Foundation.
2010.
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