Unit distance graph

Common card · No. 238900

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 two points whenever the distance between them is exactly one. To distinguish these graphs from a broader definition that allows some non-adjacent pairs of vertices to be at distance one, they may also be called strict unit distance graphs or faithful unit distance graphs. As a hereditary family of graphs, they can be characterized by forbidden induced subgraphs. The unit distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict unit distance graphs. A problem posed by Paul Erdős known as the unit distance problem asks for the maximum possible number of unit-distance pairs determined by n {\displaystyle n} points in the Euclidean plane; equivalently, it asks for the maximum number of edges in...

Read on Wikipedia · Image David Eppstein, CC0