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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 ...
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).
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 ...
Therefore, penny graphs have also been called minimum-distance graphs, [3] smallest-distance graphs, [4] or closest-pairs graphs. [5] Similarly, in a mutual nearest neighbor graph that links pairs of points in the plane that are each other's nearest neighbors , each connected component is a penny graph, although edges in different components ...
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution, from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]