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Existence of a graph with a degree sequence
The graph realization problem is a decision problem in graph theory. Given a finite sequence ( d 1 , … , d n ) {\displaystyle (d_{1},\dots ,d_{n})} of
Graph_realization_problem
Decision problem in graph theory
The digraph realization problem is a decision problem in graph theory. Given pairs of nonnegative integers ( ( a 1 , b 1 ) , … , ( a n , b n ) ) {\displaystyle
Digraph_realization_problem
Description of degree sequences of graphs
result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem, i.e. it
Erdős–Gallai_theorem
The bipartite realization problem is a classical decision problem in graph theory, a branch of combinatorics. Given two finite sequences ( a 1 , … , a
Bipartite_realization_problem
Graph with oriented edges
the directed graph.) A sequence which is the degree sequence of some directed graph, i.e. for which the directed graph realization problem has a solution
Directed_graph
Number of edges touching a vertex in a graph
sequence can be realized by a simple graph is more challenging. This problem is also called graph realization problem and can be solved by either the Erdős–Gallai
Degree_(graph_theory)
tensegrities, Cayley configuration spaces, and a variant of the graph realization problem. A distance constraint system ( G , δ ) {\displaystyle (G,\delta
Graph_flattenability
Algorithm in graph theory
The Havel–Hakimi algorithm is an algorithm in graph theory solving the graph realization problem. That is, it answers the following question: Given a finite
Havel–Hakimi_algorithm
Type of matrix
leading to more complex algorithmic tasks, such as the graph realization problem or the turnpike problem (for points on a line). By the fact that Euclidean
Euclidean_distance_matrix
Computational graph problem
point on the graph cannot see the full graph, rather only adjacent nodes or a certain "realization restriction." This optimization problem was introduced
Canadian_traveller_problem
Matrix decomposition method
Anthony Man-Cho (2007). A Semidefinite Programming Approach to the Graph Realization Problem: Theory, Applications and Extensions (PDF) (PhD). Theorem 2.2
Cholesky_decomposition
Graph divided into two independent sets
bipartite graph; in some cases, non-isomorphic bipartite graphs may have the same degree sequence. The bipartite realization problem is the problem of finding
Bipartite_graph
Graph-theoretic description of polyhedra
description of the vertex-edge graphs of these polyhedra, allowing other results on them, such as Eberhard's theorem on the realization of polyhedra with given
Steinitz's_theorem
On graph drawing with integer edge lengths
Unsolved problem in mathematics Does every planar graph have an integral Fáry embedding? More unsolved problems in mathematics In mathematics, Harborth's
Harborth's_conjecture
Branch of the mathematical field of graph theory
topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological
Topological_graph_theory
also called polyhedral graphs. The problem of deciding whether a given graph is polytopal or not is known as the realization problem and is NP hard in general
Graph_of_a_polytope
Intersection graph for curves in the plane
graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if
String_graph
Graph formed by subdivision of triangles
planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius
Apollonian_network
Theorem in graph theory
It provides one of two known approaches to solving the bipartite realization problem, i.e. it gives a necessary and sufficient condition for two finite
Gale–Ryser_theorem
Mathematical abstraction of level sets
and the Realization Problem. Discrete & Computational Geometry , 65, pp.1038-1060 L.P. Michalak, 2018. Realization of a graph as the Reeb graph of a Morse
Reeb_graph
Graph with edges of length one, able to be drawn without crossings
obtain a realization of any squaregraph as a matchstick graph. Every matchstick graph is a unit distance graph. Penny graphs are the graphs that can be
Matchstick_graph
Shortest network connecting points
geometric graphs including the relative neighborhood graph and Delaunay triangulation. By constructing the Delaunay triangulation and then applying a graph minimum
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Graph formed by touching unit circles
Whitesides, Sue (1996), "The logic engine and the realization problem for nearest neighbor graphs", Theoretical Computer Science, 169 (1): 23–37, doi:10
Penny_graph
topological graph as a topological realization of a 1-dimensional simplicial complex, it is natural to ask how the above extremal and Ramsey-type problems generalize
Topological_graph
Mathematical tree with cycle through leaves
In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four
Halin_graph
Mathematical object
recognition problem is: given a finite ASC, decide whether its geometric realization is homeomorphic to a given geometric object. This problem is undecidable
Abstract_simplicial_complex
Bipartite non-Hamiltonian polyhedral graph
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the
Herschel_graph
On tangency patterns of circles
for problems including conformal maps, polyhedral realization of graphs, the planar separator theorem, graph drawing, random walks on planar graphs, and
Circle_packing_theorem
Function type in graph theory
In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function W : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle
Graphon
Convex polytope of parenthesizations
1/2) and (1/2, 1, 1/2, 1). The convex hull of these two points is the realization of the associahedron K3. Although it lives in a 4-dimensional space,
Associahedron
Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if
Periodic_graph_(geometry)
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
Solid with twenty equal triangular faces
is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra and other
Regular_icosahedron
Prism with a 3-sided base
is identified as the unique graph with exactly three cycles that can be the outer cycle of a realization as a Halin graph. O'Keeffe & Hyde (2020), p. 139
Triangular_prism
Quantified formulas with real-number variables
natural problems in geometric graph theory, especially problems of recognizing geometric intersection graphs and straightening the edges of graph drawings
Existential theory of the reals
Existential_theory_of_the_reals
Combinitorics of Polyhedra
bipartite graph, and a linear optimization problem on this polytope can be interpreted as a bipartite minimum weight perfect matching problem. The Birkhoff–von
Polyhedral_combinatorics
Network representing spatial objects
certain metric. The simplest mathematical realization of spatial network is a lattice or a random geometric graph (see figure in the right), where nodes
Spatial_network
Family of random graph models
in the graph. In this formulation, the expected degree sequence matches the input degrees, but the actual degree sequence in any realization may vary
Configuration_model
Computational problem
computer application Pebble motion problems – Multi-robot motion planning Shortest path problem – Computational problem of graph theory Jaulin, L. (2001). "Path
Motion_planning
is a result in graph theory, a branch of combinatorics. It provides one of two known approaches solving the digraph realization problem, i.e. it gives
Fulkerson–Chen–Anstee_theorem
Study of mathematical algorithms for optimization problems
which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous
Mathematical_optimization
Irrational system of points and lines
pseudoline arrangements can be straightened into equivalent problems of visibility graph recognition. The same conversion, applied to the Perles configuration
Perles_configuration
Graph related to another graph by a covering map
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to
Covering_graph
Geometric configuration of ten points and lines
Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph
Desargues_configuration
Graph theory algorithms
Kleitman–Wang algorithms are two different algorithms in graph theory solving the digraph realization problem, i.e. the question if there exists for a finite list
Kleitman–Wang_algorithms
Theorem on graph coloring on surfaces
forms an embedding of the Heawood graph onto the torus. Grünbaum, Branko; Szilassi, Lajos (2009), "Geometric Realizations of Special Toroidal Complexes"
Heawood_conjecture
Non-orientable surface with one edge
utility graph, a six-vertex complete bipartite graph whose embedding into the Möbius strip shows that, unlike in the plane, the three utilities problem can
Möbius_strip
Process forming a path from many random steps
on a graph Self-avoiding walk – Sequence of moves on a lattice Unit root – Feature of some stochastic processes Pearson, Karl (1905). "The Problem of the
Random_walk
Conjecture on zeros of the zeta function
the quantization would be a realization of the Hilbert–Pólya program. In a connection with this quantum mechanical problem Berry and Connes had proposed
Riemann_hypothesis
Type of telecommunications engineering
process, encompassing topological design, network-synthesis, and network-realization, and is aimed at ensuring that a new telecommunications network or service
Network_planning_and_design
Symmetric bipartite cubic graph with 16 vertices and 24 edges
In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August
Möbius–Kantor_graph
Poset representing certain properties of a polytope
such as the position of vertices. A geometric polytope is said to be a realization of an abstract polytope in some real n-dimensional space, typically Euclidean
Abstract_polytope
together in some way. The most typical fuzzy set membership function has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal
Defuzzification
Pseudolines arranged largely to study arrangements of lines
These take advantage of the fact that the problem of stretchability is equivalent to the problem of the realization of a rank-3 oriented matroid. An arrangement
Arrangement_of_pseudolines
Graph with group-labeled edges
A gain graph is a graph whose edges are labelled "invertibly", or "orientably", by elements of a group G. This means that, if an edge e in one direction
Gain_graph
German mathematician (1862–1943)
L^{2}({\mathbb {R} }_{>},{\rm {d}}x)} and on compact quantum graphs with general self-adjoint realizations", Journal of Physics A: Mathematical and Theoretical
David_Hilbert
Type of mathematical set
a compact topological space which is homeomorphic to the geometric realization of a finite simplicial complex is usually called a polyhedron (see Spanier
Simplicial_complex
Model to describe distributed systems
class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements: places and transitions. Place elements are
Petri_net
Branch of mathematics
line: it gives a way to quantify the steepness of the graph of a function, even when that graph is not a straight line. In Lagrange's notation, the symbol
Calculus
Measure of network community structure
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters
Modularity_(networks)
Branch of artificial intelligence
AI planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent
Automated planning and scheduling
Automated_planning_and_scheduling
periodic graph or crystal net is ultimately mathematical (actually a crystal net is nothing but a periodic realization of an abelian covering graph over a
Periodic graph (crystallography)
Periodic_graph_(crystallography)
Abstraction of ordered linear algebra
matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane arrangements over
Oriented_matroid
Field of artificial intelligence
(AI) used graph representations and semantic networks, similar to knowledge graphs today. In such approaches, problem solving was a form of graph traversal
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
Russian mathematician (1931–2020)
solving the problem in the negative was first outlined by P. S. Novikov in his note, which appeared in 1959. However, the concrete realization of his ideas
Sergei_Adian
Method in geometry for representing a polygon by a topological skeleton
shape corresponding to this straight skeleton forms a Steinitz realization of the Halin graph formed from the tree by connecting its leaves in a cycle. Barequet
Straight_skeleton
Square matrix containing the distances between elements in a set
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken
Distance_matrix
(combinatorics) Graph structure theorem (graph theory) Grinberg's theorem (graph theory) Grötzsch's theorem (graph theory) Hajnal–Szemerédi theorem (graph theory)
List_of_theorems
Argentine-born American mathematician
1984-February 2018) and a researcher in algebraic topology, differential topology, graph theory, coding theory and combinatorial designs. He obtained a Licentiate
Italo_Jose_Dejter
Mathematical limit applied in statistical physics
for studying disordered mean-field problems. It has been devised to deal with models on locally tree-like graphs. Another alternative method is the supersymmetric
Replica_trick
Subfield of artificial intelligence
the probabilistic reasoning of ProbLog Graph Neural Networks (GNNs) are designed for tasks whose inputs are graphs and exploits the edge connections in
Neuro-symbolic_AI
Quantum variations of random walks
arbitrary graph G = ( V , E ) {\displaystyle G=(V,E)} and the discrete laplacian L Z {\displaystyle L_{\mathbb {Z} }} is replaced by the graph Laplacian
Quantum_walk
List of concepts in artificial intelligence
computational problems that can be reduced to finding good paths through graphs. anytime algorithm An algorithm that can return a valid solution to a problem even
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Strongly NP-complete problem in computer science
The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned
3-partition_problem
Japanese mathematician (born 1948)
networks in space are examples of “standard realizations”, the notion introduced by Sunada and Motoko Kotani as a graph-theoretic version of Albanese maps (Abel-Jacobi
Toshikazu_Sunada
Mathematical term in group theory
→ ∞ {\displaystyle n\to \infty } of the size of an n-ball in the Cayley graph of the group (that is, the number of elements of G that can be expressed
Grigorchuk_group
Abstraction of bar-and-joint frameworks
higher dimensions. A framework has a unique realization in d-dimensional space if every placement of the same graph with the same edge lengths is congruent
Rigidity_matroid
Vowel split in English
Trap–bath split An example of the trap–bath split Problems playing this file? See media help. The TRAP–BATH split is a vowel split that occurs mainly in
Trap–bath_split
Toroidal polyhedron with 7 faces
and 21 edges of the Szilassi polyhedron form an embedding of the Heawood graph onto the surface of a torus. Each face of this polyhedron shares an edge
Szilassi_polyhedron
Geometric concept
Unsolved problem in mathematics What is the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved
Kissing_number
Methods in artificial intelligence research
Semantic networks, conceptual graphs, frames, and logic are all approaches to modeling knowledge such as domain knowledge, problem-solving knowledge, and the
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Award for advancements in discrete mathematics
of perfect graphs. Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraic set is equivalent to the space of realizations of an oriented
Fulkerson_Prize
Convex polytope whose vertices all have integer Cartesian coordinates
convex realization is also an integer polytope and a deformation of the permutahedron. In the context of linear programming and related problems in mathematical
Integral_polytope
Unit-distance-preserving maps are isometries
Euclidean distances. Equivalently, every homomorphism from the unit distance graph of the plane to itself must be an isometry of the plane. The theorem is
Beckman–Quarles_theorem
Existence of a line through two points
all of them. It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this
Sylvester–Gallai_theorem
Flat-sided three-dimensional shape
third problem", The Mathematical Gazette, 86 (506): 241–247, doi:10.2307/3621846, JSTOR 3621846, S2CID 125593771 Grünbaum, Branko (2007), "Graphs of polyhedra;
Polyhedron
Skills, ideas and experiences
among employees can be used to construct a graph of possible knowledge flow - Tacit Knowledge Transfer Graph (TKTG). This allows one to arrange self-learning
Tacit_knowledge
Geometric structure of 8 points and 8 lines
projective configuration of type (8383). The Möbius–Kantor graph derives its name from being the Levi graph of the Möbius–Kantor configuration. It has one vertex
Möbius–Kantor_configuration
Points and lines with equal incidences
they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions: every two points of the incidence
Configuration_(geometry)
Computer that uses photons or light waves
Solving a problem with time-delays involves the following steps: Create a graph-like structure made from optical cables and splitters. Each graph has a start
Optical_computing
Techniques to study geometric data
task is to decide whether the graph has a tour whose length is at most L) belongs to the class of NP-complete problems. Thus, it is possible that the
Spatial_analysis
Sub-discipline of requirements management
tables could become very large and confusing. Traceability graph – In a traceability graph artifacts are represented as nodes. Nodes are connected by
Requirements_traceability
Property of artificial neural networks
used. Universal function approximation on graphs (or rather on graph isomorphism classes) by popular graph convolutional neural networks (GCNs or GNNs)
Universal approximation theorem
Universal_approximation_theorem
Matroid in which every permutation is a symmetry
n} -edge dipole graph, and the dual uniform matroid U n n − 1 {\displaystyle U{}_{n}^{n-1}} is the graphic matroid of its dual graph, the n {\displaystyle
Uniform_matroid
minimal surface passing through two circular wireframes. A physical realization of a minimal surface of revolution is soap film stretched between two
Minimal_surface_of_revolution
Theory of quantum gravity merging quantum mechanics and general relativity
graph-changing in order to resolve problem 3 in some sense. The master constraint algebra however is trivial and so the requirement that it be graph-changing
Loop_quantum_gravity
addresses the problem that currently, each RDF browser and visualization tool decides, on an ad hoc basis, what information in an RDF graph is presented
List_of_SIMILE_projects
Australian quantum physicist
Brendan L; Wang, Jingbo B (2008). "A classical approach to the graph isomorphism problem using quantum walks". Journal of Physics A: Mathematical and Theoretical
Jingbo_Wang
Knot invariant
In physical knot theory, each realization of a link or knot has an associated ropelength. Intuitively this is the minimal length of an ideally flexible
Ropelength
Modelling language and methodology for capturing knowledge and designing systems
of programming languages) specification for OPL and another detailed OPD graph grammar. To facilitate verification of the EBNF specification, David Shorter
Object_Process_Methodology
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
Girl/Female
Tamil
Prachiti | பà¯à®°à®šà¯€à®¤à¯€
Experience & realization
Prachiti | பà¯à®°à®šà¯€à®¤à¯€
Girl/Female
Indian
Grape like
Girl/Female
Indian
Grape vine
Girl/Female
Muslim
Grape vine
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Hindu
Wise, Knowledgeable, Attained realization
Boy/Male
Tamil
Thiru Murugan | திர௠மà¯à®°à¯à®•à®¨
Wise, Knowledgeable, Attained realization
Thiru Murugan | திர௠மà¯à®°à¯à®•à®¨
Boy/Male
Buddhist, Indian
Original Understanding; Original Realization
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Hindu
Experience & realization
Boy/Male
Indian
Realisation
Girl/Female
Muslim
Grape like
Boy/Male
Hindu, Indian, Kannada, Marathi, Tamil, Telugu, Traditional
Wise; Knowledgeable; Attained Realization
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Indian
Grape
Boy/Male
Arabic, Modern
Grape
Boy/Male
Muslim
Grape
Boy/Male
Tamil
Thirugnanam | தீரà¯à®•à¯à®¨à®¾à®¨à®®
Wise, Knowledgeable, Attained realization
Thirugnanam | தீரà¯à®•à¯à®¨à®¾à®¨à®®
Girl/Female
Hindu, Indian
Realization
Boy/Male
Hindu, Indian
Self Realization
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
Girl/Female
Muslim
One who gives light
Surname or Lastname
English
English : variant of Wickware.
Boy/Male
Australian, Czech, Czechoslovakian
Glorious Armor
Boy/Male
Muslim
Symbol, Prince, Honored, Respected
Boy/Male
Hindu
Name of Lord Vishnu, Freedom giver
Boy/Male
Assamese, Hindu, Indian, Marathi, Traditional
Lord Shiva
Girl/Female
American, Anglo, Australian, British, Christian, English, Jamaican, Portuguese
Clover; Flower Name; Fortunate; Mind; Heart; Spirit
Girl/Female
Australian, Danish, Greek
A Huntress; Immovable
Male
Scottish
Pet form of Scottish Steaphan, STEENIE means "crown."
Surname or Lastname
English
English : variant of Bailiff. See also Bayliss.
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
GRAPH REALIZATION-PROBLEM
n.
Retaliation.
n.
Anything taken from an enemy in retaliation.
n.
A sort of grape.
n.
State of being complete; fulfillment; accomplishment; realization.
n.
The act of making loyal to a king.
v. t.
Retaliation.
n.
The act of retaliating, or of returning like for like; retribution; now, specifically, the return of evil for evil; e.g., an eye for an eye, a tooth for a tooth.
n.
Retaliation.
n.
A taking by way of retaliation.
a.
Resembling a grape.
n.
The act of realizing, or the state of being realized.
n.
The act or process of idealizing.
n.
Execution; performance; realization; operation; as, the law goes into effect in May.
n.
Return or repercussion, as of sound; echo.
n.
The act of making legal.
n.
The representation of natural objects, scenes, etc., in such a way as to show their most important characteristics; the study of the ideal.
n.
Any act of retaliation.
n.
The defendant's answer to the plaintiff's replication.
n.
A repetition; a copy.