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...

are obtained if and only if the unit disk is a regular hexagon or a parallelogram, respectively. Unit disk graph Unit sphere De Branges's theorem S. Golab...

clique in the unit disk graph, so it is the clique complex or flag complex of the unit disk graph. More generally, the clique complex of any graph G is a Vietoris–Rips...

permutation graph, in turn they are a special case of the family of the complements of comparability graphs known as cocomparability graphs. A unit disk graph is...

geometric graph. For instance, the intersection graph of line segments in one dimension is an interval graph; the intersection graph of unit disks in the...

In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting...

may have different lengths. Every penny graph is a unit disk graph and a matchstick graph. Like planar graphs more generally, they obey the four color...

or polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams...

(OEIS: A029858). They are penny graphs (the contact graphs of non-overlapping unit disks in the plane), with an arrangement of disks that resembles the Sierpinski...

bandwidth allocation to radio stations, the resulting conflict graph is a unit disk graph, so the coloring problem is 3-approximable. A compiler is a computer...

^{n}} . Graphs of sphericity 1 are known as unit interval graphs or indifference graphs. Graphs of sphericity 2 are known as unit disk graphs. The sphericity...

bounded-degree planar graphs, split graphs, bipartite graphs and their complements, line graphs of bipartite graphs, unit disk graphs, interval graphs of diameter...

dimensional unit disk graphs, it is possible to transform a set of points into their indifference graph, or a set of unit intervals into their unit interval...

delivery in the so-called unit disk graph network model. Various variants, which were proposed later , also for non-unit disk graphs, are based on the principles...

graphs. The clique cover problem remains NP-complete on some other special classes of graphs, including the cubic planar graphs and unit disk graphs....

plane, that certain graphs including the polyhedral graphs have greedy embeddings in the Euclidean plane, and that unit disk graphs have greedy embeddings...

representing a graph as a unit disk graph may require exponentially many bits for the coordinates of the disk centers. Low-dimensional comparability graphs The comparability...

can be found by applying the permutation graph algorithm to each neighborhood. Similarly, in a unit disk graph (with a known geometric representation)...

metric space is a special case of a clique complex, formed from the unit disk graph of the points; however, every clique complex X(G) may be interpreted...

unit circle is called the open unit disk, while the interior of the unit circle combined with the unit circle itself is called the closed unit disk....

B.; Ravi, S. S.; Rosenkrantz, D. J. (1995). "Simple heuristics for unit disk graphs". Networks. 25 (2): 59. arXiv:math/9409226. doi:10.1002/net.3230250205...

the sensor disks as possible. By applying Menger's theorem to the unit disk graph defined from the barriers, this minimal number of disks can be shown...

approximation ratio is 2. On unit disk graphs its approximation ratio is 3. The triangular prism is the smallest graph for which one of its degeneracy...

special cases such as unit disk graphs and planar graphs. A minimum dominating set can be found in linear time in series–parallel graphs. A minimum dominating...

measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system, the base unit for length...

In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture...

graph (the study of its global connectivity) is sometimes called the Gilbert disk model after the work of Edgar Gilbert, who introduced these graphs and...

published highly-cited work on geographic routing in geometric graphs, including unit disk graphs and triangulations, with coauthors including Jit Bose, Erik...

Disk Utility is a system utility for performing disk and disk volume-related tasks on the macOS operating system by Apple Inc. The functions currently...

graphs (equivalently, unit interval graphs or proper interval graphs) have twin-width at most two. Unit disk graphs defined from sets of unit disks that...