An example of a graph that is not a unit disk graph is the star \displaystyle-free graphs", Discrete Applied Mathematics 284: 53–60, doi: 10.1016/j.dam.2020.03.024 Unit disk graphs may be formed in a different way from a collection of equal-radius circles, by connecting two circles with an edge whenever one circle contains the center of the other circle.Įvery induced subgraph of a unit disk graph is also a unit disk graph.
These graphs have a vertex for each circle or disk, and an edge connecting each pair of circles or disks that have a nonempty intersection. Unit disk graphs are the intersection graphs of equal-radius circles, or of equal-radius disks.Unit disk graphs are the graph formed from a collection of points in the Euclidean plane, with a vertex for each point and an edge connecting each pair of points whose distance is below a fixed threshold.There are several possible definitions of the unit disk graph, equivalent to each other up to a choice of scale factor:
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