realization of a graph

A realization of a graph G in a topological spaceMathworldPlanetmath X is an injective map ρ:GX such that G with the graph topology is homeomorphic to ρ(G) with the subspace topology. Of particular interest are realizations of G in 3-dimensional Euclidean spaceMathworldPlanetmath, where each of the edges is a line segmentMathworldPlanetmath, and where no 4 points of G are coplanarMathworldPlanetmath.

Title realization of a graph
Canonical name RealizationOfAGraph
Date of creation 2013-03-22 12:31:58
Last modified on 2013-03-22 12:31:58
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 7
Author rmilson (146)
Entry type Definition
Classification msc 05C99
Related topic Subdivision
Related topic GraphTopology