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Thus, it is a forbidden graph for the strict unit distance graphs, [20] but not one of the six forbidden graphs for the non-strict unit distance graphs. Other examples of graphs that are non-strict unit distance graphs but not strict unit distance graphs include the graph formed by removing an outer edge from , and the six-vertex graph formed ...
A collection of unit circles and the corresponding unit disk graph. In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a ...
In mathematics, a unit square is a square whose sides have length 1. Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0 ), (1, 0) , (0, 1) , and (1, 1) .
In graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as an intersection graph of unit spheres. The sphericity of a graph is a generalization of the boxicity and cubicity invariants defined by F.S. Roberts in the late 1960s. [1] [2] The concept of ...
H(d,1), which is the singleton graph K 1; H(d,2), which is the hypercube graph Q d. [1] Hamiltonian paths in these graphs form Gray codes. Because Cartesian products of graphs preserve the property of being a unit distance graph, [7] the Hamming graphs H(d,2) and H(d,3) are all unit distance graphs.
That is, it is a graph that has an embedding which is simultaneously a unit distance graph and a plane graph. For this reason, matchstick graphs have also been called planar unit-distance graphs. [1] Informally, matchstick graphs can be made by placing noncrossing matchsticks on a flat surface, hence the name. [2]