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...

Unit distance may refer to: Astronomical unit: the distance to the Sun Unit distance graph: a graph whose lines connect points that must be a distance...

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...

The Heawood graph is the smallest cubic graph with Colin de Verdière graph invariant μ = 6. The Heawood graph is a unit distance graph: it can be embedded...

generally, a graph is bipartite if and only if it has no odd cycles (Kőnig, 1936). Connected Eulerian Hamiltonian A unit distance graph In addition: As...

vertices and eleven edges. It can be drawn as a unit distance graph, and it requires four colors in any graph coloring. Its existence can be used to prove...

constructed it (with a non-planar embedding) as a unit distance graph that requires four colors in any graph coloring. Thus, like the simpler Moser spindle...

bipancyclic graph. can be drawn as a unit distance graph in the Euclidean plane by using the construction of the hypercube graph from subsets of a set of n elements...

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...

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ⁠ R n {\displaystyle \mathbb {R}...

property of being a unit distance graph, the Hamming graphs H(d,2) and H(d,3) are all unit distance graphs. The Hamming graphs are interesting in connection...

have equal length. That is, it is a unit distance graph. The simplest non-orientable surface on which the Petersen graph can be embedded without crossings...

concept of unit distance graph to more than 2 dimensions. In the worst case, every pair of vertices is connected, giving a complete graph. To immerse...

Euclidean complete graph. It is also possible to define graphs by conditions on the distances; in particular, a unit distance graph is formed by connecting...

Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a multiple of some base...

plane so that no two points at unit distance are the same color? More unsolved problems in mathematics In geometric graph theory, the Hadwiger–Nelson problem...

W7 is the only wheel graph that is a unit distance graph in the Euclidean plane. The chromatic polynomial of the wheel graph Wn is : P W n ( x ) = x...

the friendship graph Fn is isomorphic to the windmill graph Wd(3, n). It is unit distance with girth 3, diameter 2 and radius 1. The graph F2 is isomorphic...

Instead, its unit distance graph representation has the dihedral group Dih6 as its symmetry group. The first person to write about the Nauru graph was R. M...

graph can be represented by points in the plane in such a way that adjacent vertices are at unit distance apart; that is, it is a unit distance graph...

and a penny graph (this implies that it is unit distance and planar). It is also a 1-vertex-connected graph and a 2-edge-connected graph. There are only...

space preserves unit distances, then it preserves all Euclidean distances. Equivalently, every homomorphism from the unit distance graph of the plane to...

product of unit distance graphs is another unit distance graph. Cartesian product graphs can be recognized efficiently, in linear time. Algebraic graph theory...

shows that a graph may require very different dimensions to be represented as a unit distance graph and as a strict unit distance graph. The minimum number...

Euclidean distance is exactly one. The induced subgraphs of this graph are called unit distance graphs. A seven-vertex unit distance graph, the Moser...

complete graphs in the Diophantine plane for which the length of all edges are integers (unit distance graphs). Thus, Erdős–Diophantine graphs are exactly...

orthoschemes Hadwiger–Nelson problem on the chromatic number of unit distance graphs in the Euclidean plane Hadwiger's theorem characterizing measure...

at distance 2 {\displaystyle {\sqrt {2}}} . It can also be defined, divorced from its geometry, as an abstract undirected graph, a covering graph of the...

measure-preserving bijections from the unit interval to itself. The cut distance between two graphs is defined to be the cut distance between their associated graphons...

ISBN 978-1-58488-505-4. Horvat, Boris; Pisanski, Tomaž (2010). "Products of unit distance graphs". Discrete Mathematics. 310 (12): 1783–1792. doi:10.1016/j.disc.2009...