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mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches
Gray_graph
Scottish mathematician (1902–1979)
Telegraph. The graph is commonly known as the Gray graph. Marion Gray was born in Ayr, Scotland on 26 March 1902 to Marion (née Cameron) and James Gray. She attended
Marion_Cameron_Gray
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
Coxeter graph Tutte–Coxeter graph Dyck graph Klein graph Foster graph Biggs–Smith graph The Rado graph Folkman graph Gray graph Ljubljana graph Tutte 12-cage
List_of_graphs
Graph where all pairs of edges are automorphic
In the mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism
Edge-transitive_graph
Graph representing incident points and lines
In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points
Levi_graph
Graph with all vertices of degree 3
graphs include the Gray graph (the smallest semi-symmetric cubic graph), the Ljubljana graph, and the Tutte 12-cage. The Frucht graph is one of the five
Cubic_graph
Graph that is edge-transitive and regular but not vertex-transitive
semi-symmetric graphs after the Gray graph are the Iofinova–Ivanov graph on 110 vertices, the Ljubljana graph on 112 vertices, a graph on 120 vertices
Semi-symmetric_graph
Undirected bipartite graph with 112 vertices and 168 edges
Therefore, the Ljubljana graph is a semi-symmetric graph, the third smallest possible cubic semi-symmetric graph after the Gray graph on 54 vertices and the
Ljubljana_graph
Basic concept of graph theory
mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that
Connectivity_(graph_theory)
chains Examples of vector spaces Fano plane Frieze group Gray graph Hall–Janko graph Higman–Sims graph Hilbert matrix Illustration of a low-discrepancy sequence
List_of_mathematical_examples
Writing paper with a grid
quadrillé, 'large square', is a common form of graph paper with a sparse grid printed in light blue or gray and right to the edge of the paper. In the U
Graph_paper
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
Path in a graph that visits each vertex exactly once
the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly
Hamiltonian_path
the graph is planar and F indicates that the graph is not planar. Wikimedia Commons has media related to Graphs by number of vertices. See also Graph theory
List of graphs by edges and vertices
List_of_graphs_by_edges_and_vertices
Open problem in graph theory
sequence of some graph. Note that the term sometimes allows a multigraph, but here it is defined as the degree sequence of a simple graph. A graph G {\displaystyle
Imbalance_conjecture
Trail in a graph that visits each edge once
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)
Eulerian_path
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
Semi-symmetric cubic graph with 110 vertices and 165 edges
110-vertex Iofinova–Ivanov graph is, in graph theory, a semi-symmetric cubic graph with 110 vertices and 165 edges. The graph is named after Marina Evgenievna
110-vertex Iofinova–Ivanov graph
110-vertex_Iofinova–Ivanov_graph
Radcliffe College Marion Cameron Gray (1902–1979), Scottish telephone engineer, discoverer of the Gray graph Mary W. Gray (born 1939), author on mathematics
List_of_women_in_mathematics
Cartesian product of complete graphs
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science
Hamming_graph
possible cubic semi-symmetric graph after the Gray graph, the Iofinova–Ivanov graph on 110 vertices, the Ljubljana graph and a graph on 120 vertices with girth
Tutte_12-cage
Cycles in a graph that cover each edge twice
In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly
Cycle_double_cover
In mathematics, a k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended
Homogeneous_graph
American mathematician and historian (1898–1984)
(1930): 357–365. Funkhouser, H. Gray. "A note on a tenth century graph." Osiris (1936): 260–262. Funkhouser, H. Gray. "Historical development of the graphical
Howard_G._Funkhouser
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
Slovenian mathematician
and half-transitive graphs. With co-authors, he proved that the Gray graph on 54 vertices is the smallest cubic semi-symmetric graph. He has well over 100
Dragan_Marušič
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Representation of cubic graphs
In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert
LCF_notation
Ordering of binary values, used for positioning and error correction
n-dimensional hypercube graph, and coil-in-the-box codes, or coils, are the sequences of nodes of induced cycles in a hypercube. Viewed as Gray codes, these sequences
Gray_code
Structure that represents calling relationships between subroutines in a computer program
A call graph (also known as a call multigraph) is a directed graph that represents calling relationships between subroutines in a computer program. Each
Call_graph
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Distance from a point to the boundary of a set
The graph (bottom, in red) of the signed distance between the points on the xy plane (in blue) and a fixed disk (also represented on top, in gray)
Signed_distance_function
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
lecturer in geology to the British Museum Marion Cameron Gray 1902–1979 mathematician discovered Gray graph David Gregory 1659–1708 astronomer, mathematician
List_of_Scottish_scientists
American baseball player (born 1997)
Retrieved September 22, 2021. "Splits Leaderboards | FanGraphs". www.fangraphs.com. "Josiah Gray Stats, Height, Weight, Position, Rookie Status & More"
Josiah_Gray
British mathematician (born 1943)
from the Mathematical Intelligencer (with J. Gray), Springer, 2000: ISBN 0-387-98686-3 An Atlas of Graphs (with Ronald Read), Oxford: Clarendon Press,
Robin_Wilson_(mathematician)
Graph describing a topological embedding
In topological graph theory, a graph-encoded map or gem is a method of encoding a cellular embedding of a graph using a different graph with four vertices
Graph-encoded_map
Combinatorial representation of a graph on an orientable surface
a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding, a rotation system, an orientable ribbon graph, a
Combinatorial_map
American computer scientist and Internet pioneer (born 1943)
Vinton Gray Cerf (/sɜːrf/; born June 23, 1943) is an American Internet pioneer and is recognized as one of "the fathers of the Internet", sharing this
Vint_Cerf
Geometry with 7 points and 7 lines
particular graph is a connected cubic graph (regular of degree 3), has girth 6 and each part contains 7 vertices. It is the Heawood graph, the unique
Fano_plane
Timing imbalance of energy demand and solar power generation
The duck curve is a graph showing the electricity demand remaining after subtracting electricity supplied by variable renewable energy sources (primarily
Duck_curve
Mathematical puzzle game
undirected graph, the nodes representing distributions of disks and the edges representing moves. For one disk, the graph is a triangle: The graph for two
Tower_of_Hanoi
Problem in graph theory
finite connected vertex-transitive graph contain a Hamiltonian path? More unsolved problems in mathematics In graph theory, the Lovász conjecture (1969)
Lovász_conjecture
measure, abolishing term limits for all elected positions. The following graph shows the margin of victory of the Democratic Party over the runner-up in
Mayoral elections in Washington, D.C.
Mayoral_elections_in_Washington,_D.C.
Polygenic phenotypic characteristic
(2003). "An Ocularist's Approach to Human Iris Synthesis". IEEE Comput. Graph. Appl. 23 (6): 70–5. doi:10.1109/MCG.2003.1242384. S2CID 537404. "Where
Eye_color
Instantaneous rate of change (mathematics)
chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation
Derivative
Automated methods for the creation of mazes
between them. This predetermined arrangement can be considered as a connected graph with the edges representing possible wall sites and the nodes representing
Maze_generation_algorithm
Class of hand-held calculator
A graphing calculator is a class of hand-held calculator that is capable of plotting graphs and solving complex functions. While there are several companies
Comparison of HP graphing calculators
Comparison_of_HP_graphing_calculators
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
British political scandal
Sue Gray. In January 2022, the Metropolitan Police opened its own investigation into potential breaches of COVID-19 regulations, which delayed Gray's report
Partygate
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
Conjecture in graph theory
\tau (H)\leq (r-1)\cdot \nu (H)} More unsolved problems in mathematics In graph theory, Ryser's conjecture is a conjecture relating the maximum matching
Ryser's_conjecture
In graph theory, a maximally matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching in the graph. An alternative
Maximally_matchable_edge
Search engine from Google
the feature expanded to all countries globally in 2017. The Knowledge Graph is a knowledge base used by Google to enhance its search engine's results
Google_Search
English presenter (born 1980s)
Graph Search tool causes increasing privacy concerns". The Guardian. Archived from the original on 8 February 2014. Retrieved 25 January 2013. Gray,
Tom_Scott_(presenter)
Diagrammatic representation of Sun's position over a period of time
Earth at the same clock time every day for an entire year, or by plotting a graph of the Sun's declination against the equation of time. The resulting curve
Analemma
Free online crowdsourced encyclopedia
be due to errors in counting, other experts feel that Google's Knowledge Graphs project launched last year may be gobbling up Wikipedia users." When contacted
Wikipedia
Set of random variables
of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it
Markov_random_field
Transformation defined on a grayscale image
of ridges. There are different technical definitions of a watershed. In graphs, watershed lines may be defined on the nodes, on the edges, or hybrid lines
Watershed_(image_processing)
2025 operating system version
Sur; an icon that does not comply with the requirement is placed inside a gray squircle. Areas such as the Control Center, app opening, and Spotlight Search
MacOS_Tahoe
Network that allows computers to share resources and communicate with each other
science Theory Graph Complex network Contagion Small-world Scale-free Community structure Percolation Evolution Controllability Graph drawing Social capital
Computer_network
Computer scientist and engineer
systems are necessary for graph computation. GraphX was released as an open source project and merged into Spark in 2014, as the graph processing library on
Reynold_Xin
Knowledge Graph which when clicked, makes confetti explode. "panipuri( see it )" will show three types of panipuris in the Knowledge Graph, which when
List_of_Google_Easter_eggs
firms that tend to inflate electoral rating of United Russia are colored in gray. Polling firms affiliated with Russian liberal opposition are colored in
Opinion polling for the 2026 Russian legislative election
Opinion_polling_for_the_2026_Russian_legislative_election
Public school district in Riverdale, Iowa, United States
This graph was using the legacy Graph extension, which is no longer supported. It needs to be converted to the new Chart extension.
Pleasant Valley Community School District
Pleasant_Valley_Community_School_District
Major League Baseball team season
Retrieved September 25, 2026. "2026 Chicago White Sox Schedule & Results". FanGraphs. Retrieved May 26, 2026. "2025 Chicago White Sox Statistics". Baseball-Reference
2026_Chicago_White_Sox_season
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
Hoffman (1944), mathematician known for constructing the Hoffman–Singleton graph Bruce Mazlish (1944), historian and professor at Massachusetts Institute
List of Columbia College people
List_of_Columbia_College_people
Global system of connected computer networks
International Telecommunication Union (ITU). Retrieved 25 May 2015. Internet users graphs Archived 9 May 2020 at the Wayback Machine, Market Information and Statistics
Internet
Triangulation method
incremental Voronoi insertion Gabriel graph Gradient pattern analysis Hamming bound – sphere-packing bound Linde–Buzo–Gray algorithm Lloyd's algorithm – Voronoi
Delaunay_triangulation
Series of graphing calculators
The TI-Nspire is a graphing calculator line made by Texas Instruments, with the first version released on 25 September 2007.[better source needed] The
TI-Nspire_series
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
Algorithmic application of graph theory
blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based
Connected-component_labeling
Coronet Films; the Chudnovsky brothers; fractals come from plotting on a graph imaginary numbers against real numbers and have self-similarity, and Ian
List_of_Equinox_episodes
Yasyazaru in Baki the Grappler, Trailmon in Digimon Frontier, Nishiya in Speed Grapher, Taiin in Code Geass), dies at age 57. November 13: Dan Hennessey, Canadian
2024_in_animation
Overview of democracy measures
Unraveling The Democratic Era?" (PDF). Retrieved 17 March 2026. "Country Graph". V-Dem Institute. March 2026. Archived from the original on 1 March 2026
Democracy_indices
in a 2-category were to be a 2-graph morphism from some 2-graph (that is 2-globular set) into the underlying 2-graph of the 2-category, then in the left-hand
Pasting_theorem
Cycle through all length-k sequences
an n-dimensional de Bruijn graph over k symbols (or equivalently, an Eulerian cycle of an (n − 1)-dimensional de Bruijn graph). An alternative construction
De_Bruijn_sequence
Sensory organ of vision
(2003). "An Ocularist's Approach to Human Iris Synthesis". IEEE Comput. Graph. Appl. 23 (6): 70–5. doi:10.1109/MCG.2003.1242384. Zhu, Gu; Evans, David
Human_eye
Ghanaian politician (1909–1972)
recovering strongly in most advanced economies". Economic Policy Reforms 2019 (graph). Organisation for Economic Co-operation and Development. 2019. doi:10.1787/888933954135
Kwame_Nkrumah
Operating system that behaves similarly to Unix
The Linux Information Project (LINFO) UNIX history – a history time line graph of most UNIX and Unix-like systems by Éric Lévénez Grokline's UNIX Ownership
Unix-like
bsdiff binary patch 7C 61 8A B2 |aŠ² 0 hpapp hpprgm hpsettings HP Prime graphing calculator file 43 5A 50 58 CZPX 0 czx Czip X encrypted archive (v4.x)
List_of_file_signatures
Adventure, Tactical RPG Red Entertainment, Sega Saturn Sakura Taisen Teigeki Graph Non-game Segata Sanshirou Shinken Yuugi Mini games Ecole Software Sega Touring
List_of_Sega_video_games
industrialization, 1810s-1840s. By the late-1800s, wood ("biomass" in the graphs) began to decline as the nation's energy demands soared and forests near
Environmental history of the United States
Environmental_history_of_the_United_States
Topics referred to by the same term
States Navy patrol boat in commission from 1917 to 1919 Snark (graph theory), a type of graph SNARK (theorem prover), a computer program zk-SNARK, zero-knowledge
Snark
Critical point on a surface graph which is not a local extremum
mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are
Saddle_point
Statistical law in machine learning
MLP-mixers, recurrent neural networks, convolutional neural networks, graph neural networks, U-nets, encoder–decoder (and encoder-only) (and decoder-only)
Neural_scaling_law
President of the United States from 2009 to 2017
slightly apart". The New York Times. p. A1. Retrieved January 30, 2010. Gray, Steven (September 10, 2008). "Taking professor Obama's class". Time. Archived
Barack_Obama
Graphic visual representation of information
are commonly used to show the weather, as well as maps, site plans, and graphs for summaries of data. Some books are almost entirely made up of information
Infographic
Network service attack performed by multiple fake identities
approaches to Sybil attack prevention include identity validation, social trust graph algorithms, economic costs, personhood validation, and application-specific
Sybil_attack
Network for communications over distance
science Theory Graph Complex network Contagion Small-world Scale-free Community structure Percolation Evolution Controllability Graph drawing Social capital
Telecommunications_network
American computer scientist and professor
systems, with contributions to stream databases, distributed databases, graph databases, and column-store databases. He helped create C-Store, a column-oriented
Daniel_Abadi
Retail store for Google hardware products
"distinctly Google", with visual aesthetics featuring "light wood grain and gray fabric pairing up with playful hints of bright colors", along with "custom-created
Google_Store
Convex polytope, the n-dimensional analogue of a square and a cube
an example of a zonotope. The 1-skeleton of a hypercube is a hypercube graph. A unit hypercube of dimension n {\displaystyle n} is the convex hull of
Hypercube
Wiskott, Laurenz; et al. (1997). "Face recognition by elastic bunch graph matching". IEEE Transactions on Pattern Analysis and Machine Intelligence
List of datasets in computer vision and image processing
List_of_datasets_in_computer_vision_and_image_processing
Graph: things, not strings". The Official Google Blog. Retrieved February 2, 2014. Sullivan, Danny (May 16, 2012). "Google Launches Knowledge Graph To
Timeline of web search engines
Timeline_of_web_search_engines
Level of ease with which a reader can understand written text
teaching English teachers in Uganda, Edward Fry developed his Readability Graph. It became one of the most popular formulas and easiest to apply. The automated
Readability
Atrocities by Vetoing UN Resolution". Fars News Agency. 9 December 2023. Gray, Andrew. "EU's Borrell suggests US cut military aid to Israel". Reuters.
United States support for Israel in the Gaza war
United_States_support_for_Israel_in_the_Gaza_war
Visual representation of data
the original on 2014-04-14. Funkhouser, Howard Gray (January 1936). "A Note on a Tenth Century Graph". Osiris. 1: 260–262. doi:10.1086/368425. JSTOR 301609
Data and information visualization
Data_and_information_visualization
travel, tourism, insurance
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travel, tourism, insurance