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See searches and references containing UNIT DISTANCE-GRAPH!UNIT DISTANCE-GRAPH
Geometric graph with unit edge lengths
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_graph
Topics referred to by the same term
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
Unit_distance
Graph with edges of length one, able to be drawn without crossings
That is, it is a graph that has an embedding which is simultaneously a unit distance graph and a plane graph. Informally, matchstick graphs can be made by
Matchstick_graph
Intersection graph of unit disks in the plane
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
Unit_disk_graph
Graph with nodes connected in a closed chain
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
Cycle_graph
Undirected unit-distance graph requiring four colors
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
Golomb_graph
Undirected unit-distance graph requiring four colors
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
Moser_spindle
Cartesian product of complete graphs
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
Hamming_graph
Cubic graph with 10 vertices and 15 edges
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
Petersen_graph
Mathematical problem
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
Hadwiger–Nelson_problem
Measurement scale based on orders of magnitude
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
Logarithmic_scale
Graphs formed by a hypercube's edges and vertices
thus a 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
Hypercube_graph
Undirected graph with 14 vertices
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
Heawood_graph
Planar graph with 5 nodes and 6 edges
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
Butterfly_graph
Graph whose embedding in a Euclidean space forms a regular tiling
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}
Lattice_graph
Graph of triangles with a shared vertex
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
Friendship_graph
Study of graphs defined by geometric means
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
Geometric_graph_theory
Cycle graph plus universal vertex
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
Wheel_graph
Family of cubic graphs formed from regular and star polygons
n , 4 ) {\displaystyle G(n,4)} . Every generalized Petersen graph is a unit distance graph. G ( n , k ) {\displaystyle G(n,k)} is isomorphic to G ( n
Generalized_Petersen_graph
Unit-distance-preserving maps are isometries
space preserves unit distances, then it preserves all Euclidean distances. Equivalently, every homomorphism from the unit distance graph of the plane to
Beckman–Quarles_theorem
24-vertex symmetric bipartite cubic graph
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
Nauru_graph
Function type in graph theory
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
Graphon
Periodic spatial graph
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
Laves_graph
Graph formed by touching unit circles
In geometric graph theory, a penny graph is a contact graph of unit circles. It is formed from a collection of unit circles that do not cross each other
Penny_graph
Operation in graph theory
(G)\gamma (H).} The Cartesian product of unit distance graphs is another unit distance graph. Cartesian product graphs can be recognized efficiently, in linear
Cartesian_product_of_graphs
Integer associated with a graph
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
Dimension_(graph_theory)
Family of graphs with 2n nodes and n(n-1) edges
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
Crown_graph
On coloring infinite graphs
Euclidean distance is exactly one. The induced subgraphs of this graph are called unit distance graphs. A seven-vertex unit distance graph, the Moser
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Intersection graph of unit intervals on the real line
their numbers are within one unit of each other. An indifference graph is also the intersection graph of a set of unit intervals, or of properly nested
Indifference_graph
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Graph with a triangular truncated trapezohedron as its skeleton
a symmetry of the graph. The Dürer graph is a unit distance graph. However, although the Dürer graph is planar, its unit-distance embedding has crossings
Dürer_graph
Cubic distance-regular graph with 102 nodes and 153 edges
Biggs–Smith graph is 3. The chromatic index of the Biggs–Smith graph is 3. The Biggs–Smith graph is a unit-distance graph. The Biggs–Smith graph is an order-17
Biggs–Smith_graph
Distance from center of Earth to center of Moon
characteristic distance, is a unit of measure in astronomy. More technically, it is the semi-major axis of the geocentric lunar orbit. The average lunar distance is
Lunar_distance
Solid with six equal square faces
hypercube graph, it has a cycle which visits every vertex exactly once, and it is also an example of a unit distance graph. The cubical graph is bipartite
Cube
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
Gray_graph
of unit distance graphs Jaeger's Petersen-coloring conjecture: every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph The
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Symmetric bipartite cubic graph with 16 vertices and 24 edges
Since the hypercube is a unit distance graph, the Möbius–Kantor graph can also be drawn in the plane with all edges unit length, although such a drawing
Möbius–Kantor_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
of the Holt graph is 3. The chromatic index of the Holt graph is 5. The Holt graph is Hamiltonian. The Holt graph is a unit distance graph. Doyle, P. "A
Holt_graph
Square matrix containing the distances between elements in a set
computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between
Distance_matrix
Measure of distance in physical space
of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for
Length
Type of metric geometry
Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance. The name refers to the
Taxicab_geometry
Separation between two points
ways, including Levenshtein distance, Hamming distance, Lee distance, and Jaro–Winkler distance. In a graph, the distance between two vertices is measured
Distance
Complete graph on the integer plane which cannot be expanded
complete graphs in the Diophantine plane for which the length of all edges are integers (unit distance graphs). Thus, Erdős–Diophantine graphs are exactly
Erdős–Diophantine_graph
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Tiling of the plane with 60° rhombi
Manhattan distance between the corresponding lattice points. Thus, the rhombille tiling can be viewed as an example of an infinite unit distance graph and partial
Rhombille_tiling
Number of vertices with unambiguous distances
vertices are uniquely determined by their distances to the vertices in S. Finding the metric dimension of a graph is an NP-hard problem; the decision version
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
bipartite graphs are hom-equivalent. The core of each of these graphs is the two-vertex complete graph K2. By the Beckman–Quarles theorem, the infinite unit distance
Core_(graph_theory)
English biogerontologist and author (born 1963)
2018, de Grey posted a paper to arXiv explicitly constructing a unit-distance graph in the plane that cannot be colored with fewer than five colors,
Aubrey_de_Grey
In graph theory, the mathematically simplest spatial network
if and only if their distance is in a given range, e.g. smaller than a certain neighborhood radius, r. Random geometric graphs resemble real human social
Random_geometric_graph
Graph with nodes connected linearly
In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that
Path_graph
Topics referred to by the same term
to: Distance function, defines a distance between each pair of elements of a set Distance (graph theory), the distance between two vertices in a graph Cosmic
Distance_(disambiguation)
Computational problem of graph theory
problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length or distance of each
Shortest_path_problem
windmill graph D(3,21) 1744 = k such that k, k+1 and k+2 are sums of 2 squares 1745 = 5-Knödel number 1746 = number of unit-distance graphs on 8 nodes
1000_(number)
Python library for graphs and networks
control the distance between nodes with the k parameter or decide how many iterations the simulation should run. It lets you lay out the graph in more than
NetworkX
Puzzle
reduction from finding Hamiltonian cycles in integer-coordinate unit distance graphs. There is a solution using integer linear programming in the MathProg
Hashiwokakero
American mathematician (born 1998)
conjecture on unit distance graphs. GPT-5 provided a method to construct n points in the plane from which Ω(n1+ε) pairs of points are unit distance apart, for
Mehtaab_Sawhney
Geometric notation for congruent line segments
as: Unit and value marks — as on a ruler or number line Congruence notation in geometry — as on a geometric figure Graphed points — as on a graph Hatch
Hatch_mark
Open source routing engine
Besides point-to-point routing for different vehicles GraphHopper can be used to calculate distance matrices which are then used as an input for vehicle
GraphHopper
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
Graph operation
Moser spindle, a seven-vertex unit distance graph that requires four colors. As another example, if G and H are cycle graphs of length p and q respectively
Hajós_construction
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
Computer science metric of string similarity
Levenshtein distance and LCS distance with unit cost satisfy the above conditions, and therefore the metric axioms. Variants of edit distance that are not
Edit_distance
Measure of similarity and diversity between sets
In practice, graph representations like adjacency lists are used to improve the efficiency of intersection and union math. For large graphs, computing similarity
Jaccard_index
On graph drawing with integer edge lengths
planar graph have an integral Fáry embedding? More unsolved problems in mathematics In mathematics, Harborth's conjecture states that every planar graph has
Harborth's_conjecture
Magnitude of velocity
position per unit of time, it is thus a non-negative scalar quantity. The average speed of an object in an interval of time is the distance travelled by
Speed
Parallel version of breadth-first search algorithm
explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance
Parallel_breadth-first_search
Graph used in computational complexity theory and graph theory
}^{n}} is the graph on the 2n vertices of an n-dimensional unit hypercube [0,1]n in which two vertices are adjacent when their Hamming distance (the number
Frankl–Rödl_graph
Set of points at distance less than one from a given point
mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1:
Unit_disk
including the unit distance graph problem, the planar segment-center problem, and the finding of Davenport–Schinzel sequences. Ordered graph Graph coloring
Interval_coloring
Tree graph with one central node and leaves of length 1
In graph theory, the star Sk is the complete bipartite graph K1, k, that is, it is a tree with one internal node and k leaves. Alternatively, some authors
Star_(graph_theory)
Geometry problem
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean
Distance from a point to a line
Distance_from_a_point_to_a_line
Graphical representation of data
A chart (sometimes known as a graph) is a graphical representation for data and information visualization, in which "the data is represented by symbols
Chart
Planar graph with 4 nodes and 5 edges
mathematical field of graph theory, the diamond graph is a planar, undirected graph with 4 vertices and 5 edges. It consists of a complete graph K 4 {\displaystyle
Diamond_graph
Mathematical model used by graph-oriented databases
A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated
Property_graph
Shortest network connecting points
as the minimum spanning tree of a complete graph with the points as vertices and the Euclidean distances between points as edge weights. The edges of
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
On sets of points with integer distances
a point set forms an Erdős–Diophantine graph, an inextensible system of integer points with integer distances. The Erdős–Anning theorem inspired the Erdős–Ulam
Erdős–Anning_theorem
Geometric graph connecting nearby points
set. Because it is defined only in terms of the distances between points, the relative neighborhood graph can be defined for point sets in any dimension
Relative_neighborhood_graph
Length of a line segment
that preserves unit distances must be an isometry, preserving all distances. In many applications, and in particular when comparing distances, it may be more
Euclidean_distance
Grünbaum. The Levi graph of the configuration is the Kronecker cover of the odd graph O4, and is isomorphic to the middle layer graph of the seven-dimensional
Danzer's_configuration
Circle with radius of one
called the closed unit disk. One may also use other notions of "distance" to define other "unit circles", such as the Riemannian circle; see the article on
Unit_circle
Graph path which is an induced subgraph
perfect graph theorem, the perfect graphs are the graphs with no odd hole and no odd antihole. The distance-hereditary graphs are the graphs in which
Induced_path
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Least-weight tree connecting graph vertices
tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the
Minimum_spanning_tree
Topics referred to by the same term
orthoschemes Hadwiger–Nelson problem on the chromatic number of unit distance graphs in the Euclidean plane Hadwiger's theorem characterizing measure
Hadwiger_conjecture
of 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
Sphericity_(graph_theory)
Archimedean solid with 62 faces
rhombicosidodecahedron is the common distance of these points from the origin, namely √φ6+2 = √8φ+7 for edge length 2. For unit edge length, R must be halved
Rhombicosidodecahedron
Largest distance between two points
vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs. Researchers
Diameter_of_a_set
Quantified formulas with real-number variables
square container. recognition of unit distance graphs, and testing whether the dimension or Euclidean dimension of a graph is at most a given value. stretchability
Existential theory of the reals
Existential_theory_of_the_reals
Topological space formed from distances
pair of points that are at unit distance or less in the given metric space. As such, its 1-skeleton is the unit disk graph of its points. It contains
Vietoris–Rips_complex
the mathematics of infinite graphs, an end of an undirected graph represents, intuitively, a direction in which the graph extends to infinity. Ends may
End_(graph_theory)
Software design structured around a node graph
units. Node graphs are a type of visual programming language. The source code for the software application is organized into atomic functional units called
Node_graph_architecture
Type of crystal structure
The first-, second-, third-, fourth-, and fifth-nearest-neighbor distances in units of the cubic lattice constant are 3 4 , 2 2 , 11 4 , 1 , 19 4 , {\displaystyle
Diamond_cubic
Limit of the tangent line at a point that tends to infinity
oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x
Asymptote
Chordal graph where all cycles of even length have odd chords
are an odd distance (>1) apart from each other in the cycle. Strongly chordal graphs have a forbidden subgraph characterization as the graphs that do not
Strongly_chordal_graph
Structure from which the geometry of the universe arises
fundamental unit of volume to a classical large scale continuous space. Random graphs by Antonsen Spacetime is described by dynamical graphs with points
Pregeometry_(physics)
Cost added by producing one additional unit of a product or service
additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as
Marginal_cost
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
Girl/Female
Arabic, Muslim, Sindhi
Some Distance
Girl/Female
Muslim
Some distance
Girl/Female
Indian
Some distance
Male
English
Variant spelling of English Unni, UNI means "afflicted, depressed."
Girl/Female
Arabic, Muslim, Sindhi
Some Distance
Boy/Male
Indian
Distance
Girl/Female
Indian
Some distance
Female
Hebrew
(×וּרִית) Hebrew name URIT means "fire, light."
Girl/Female
Muslim/Islamic
Some distance
Girl/Female
English French
Certain fortune; fate. The mythological Greek god of fate.
Boy/Male
Arabic
Distance
Girl/Female
Muslim
Some distance
Girl/Female
Muslim
Some distance
Girl/Female
Tamil
A unit of measure for long distances, A plan
Girl/Female
Muslim
Some distance
Female
Welsh
Variant spelling of Welsh Enid, ENIT means "soul."
Girl/Female
Muslim/Islamic
Some distance
Girl/Female
Hindu
A unit of measure for long distances, A plan
Female
English
English name derived from the vocabulary word, UNITY means "oneness, unity."
Female
French
French form of Latin Constantia, CUSTANCE means "steadfast."Â
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
Girl/Female
Spanish English French
Joy.
Boy/Male
Tamil
Ramatasan | ரமாஂதாஸநÂ
Boy/Male
Hindu, Indian
Beautiful
Girl/Female
Irish
Helmet.
Boy/Male
Arabic, Muslim
Ease; Convenience
Boy/Male
Muslim
One who presents
Girl/Female
Christian, English, Irish
Shining; Sea Bright
Boy/Male
Indian
Jungle, Forest
Boy/Male
Muslim
Aim. Friendship.
Male
Arthurian
, (Sir); son of king Uriens.
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
UNIT DISTANCE-GRAPH
v. t.
To remove the turns of (a rope or cable) from the bits; as, to unbit a cable.
a.
Indistinct; faint; obscure, as from distance.
v. t.
To unite.
n.
Remoteness in succession or relation; as, the distance between a descendant and his ancestor.
v. t.
To cause to appear as if at a distance; to make seem remote.
n.
Concord; harmony; conjunction; agreement; uniformity; as, a unity of proofs; unity of doctrine.
imp. & p. p.
of Knit
n.
Distance.
a.
Separated; having an intervening space; at a distance; away.
a.
Far separated; far off; not near; remote; -- in place, time, consanguinity, or connection; as, distant times; distant relatives.
n.
Any one of numerous species of fresh-water mussels belonging to Unio and many allied genera.
v. t.
To unite closely; to connect; to engage; as, hearts knit together in love.
n.
The interval between two notes; as, the distance of a fourth or seventh.
v. t.
To put together so as to make one; to join, as two or more constituents, to form a whole; to combine; to connect; to join; to cause to adhere; as, to unite bricks by mortar; to unite iron bars by welding; to unite two armies.
v. t.
To unite closely; to knit together.
v. t.
To outstrip by as much as a distance (see Distance, n., 3); to leave far behind; to surpass greatly.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
v. t.
United; joint; as, unite consent.
v. t.
To place at a distance or remotely.
imp. & p. p.
of Distance