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mathematical field of graph theory, the Hoffman graph is a 4-regular graph with 16 vertices and 32 edges discovered by Alan Hoffman. Published in 1963,
Hoffman_graph
7-regular undirected graph with 50 nodes and 175 edges
of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with
Hoffman–Singleton_graph
Regular graph with girth more than twice its diameter
graph. Moore graphs were named by Hoffman & Singleton (1960) after Edward F. Moore, who posed the question of describing and classifying these graphs
Moore_graph
Nauru graph and the Desargues graph are integral. The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande
Integral_graph
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12
List_of_graphs
Concept in graph theory
graph on GQ(2, 4). The Hoffman–Singleton graph is an srg(50, 7, 0, 1). The Gewirtz graph is an srg(56, 10, 0, 2). The M22 graph aka the Mesner graph is
Strongly_regular_graph
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
It is a subgraph of the Hoffman–Singleton graph. Brouwer, A. E.; Cohen, A. M.; Neumaier, A. (1989), Distance-regular graphs, Springer-Verlag, Theorem
Sylvester_graph
American businessman
acting as a CEO for a company called SafeGraph until October 2024, when he stepped down and remained chairman. Hoffman was a contributor to the Huffington
Auren_Hoffman
two in the group of automorphisms of the Hoffman–Singleton graph. Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new
Higman–Sims_graph
Mathematical Graph
as generalizing symmetric graphs, that is, graphs that are both vertex- and edge-transitive. For example, the Hoffman graph is 1-walk-regular but not
Walk-regular_graph
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
Graph representing edges of another graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges
Line_graph
Cubic graph with 28 vertices and 42 edges
6-cycles. The Coxeter graph may be derived from the Hoffman-Singleton graph. Take any vertex v in the Hoffman-Singleton graph. There is an independent
Coxeter_graph
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Graph linking pairs of comparable elements in a partial order
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability
Comparability_graph
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
Linear algebra aspects of graph theory
regular graphs, originally due to Alan J. Hoffman and Philippe Delsarte. Suppose that G {\displaystyle G} is a k {\displaystyle k} -regular graph on n {\displaystyle
Spectral_graph_theory
American mathematician (1924–2021)
of graphs. Hoffman and Robert Singleton constructed the Hoffman–Singleton graph, which is the unique Moore graph of degree 7 and diameter 2. Hoffman died
Alan_J._Hoffman
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
Finding the largest graph of given diameter and degree
bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and
Degree_diameter_problem
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Symmetric bipartite cubic graph with 16 vertices and 24 edges
graph also occurs many times as an induced subgraph of the Hoffman–Singleton graph. Each of these instances is in fact an eigenvector of the Hoffman-Singleton
Möbius–Kantor_graph
Intersection graph for intervals on the real number line
intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring
Interval_graph
(2012). The Hoffman–Singleton graph. Graph found by Sampels (1997). Graph found by Dinneen & Hafner (1994). Graphs found by Storwick (1970). Graph found by
Table of the largest known graphs of a given diameter and maximal degree
Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree
American mathematician (1949–2022)
Dean Gunnar Hoffman (May 8, 1949 – November 11, 2022) was an American mathematician who worked primarily in graph theory, design theory, number theory
Dean_G._Hoffman
Petersen graph (degree three), and the Hoffman–Singleton graph (degree seven). Only one more of these Moore graphs can exist, with degree 57. For all other
McKay–Miller–Širáň_graph
Hungarian mathematician (1913–1996)
Man Who Loved Only Numbers, public lecture by Paul Hoffman "Open problems of Paul Erdős in graph theory" by Fan Chung Portals: Biography Hungary Mathematics
Paul_Erdős
US EPA program and certification
2015 graph showing cities with the most Energy Star-certified buildings
Energy_Star
Graph whose shortest paths are unique
Hoffman–Singleton graph. Despite additional research on the properties such a graph must have, it is not known whether there are more of these graphs
Geodetic_graph
Pandemic caused by SARS-CoV-2
marked by spike in world hunger". who.int. Retrieved 14 December 2021. Hoffman JA, Miller EA (August 2020). "Addressing the Consequences of School Closure
COVID-19_pandemic
Tabular arrangement of the chemical elements
(1): 83–116. Bibcode:2002ADNDT..80...83T. doi:10.1006/adnd.2001.0873. Hoffman, D. C.; Lawrence, F. O.; Mewherter, J. L.; Rourke, F. M. (1971). "Detection
Periodic_table
Quality in crops
was not done under fresh water conditions but in saline conditions. #) Graphs with scatter plots are shown in the report for these two varieties only
Crop_tolerance_to_seawater
Professional network website
200 countries and territories. It was launched on May 5, 2003, by Reid Hoffman and Eric Ly, receiving financing from numerous venture capital firms, including
English philosopher and logician (1872–1970)
Theory of relations Type theory / ramified type theory Tensor product of graphs Unity of the proposition Member of the House of Lords Lord Temporal Hereditary
Bertrand_Russell
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
proven in Schrijver (1998). 6. Hoffman and Kruskal proved the following theorem. Suppose G {\displaystyle G} is a directed graph without 2-dicycles, P {\displaystyle
Unimodular_matrix
American mathematician
areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree
Fan_Chung
American mathematician and computer scientist
the same degree. The graphs matching this bound were named Moore graphs by Hoffman & Singleton (1960). With Claude Shannon, before and during his time
Edward_F._Moore
American pharmaceutical company (1892–2019)
Hooked On OxyContin, Christine Willmsen, Feb. 1, 2019. This article includes graph which shows with and without OxyContin "Savings Card." Kassie McClung (The
Purdue_Pharma
Music database and statistics website
A second round was led by Stefan Glaenzer, joined by Joi Ito and Reid Hoffman, who also purchased shares from Michael Breidenbruecker. In 2006, the company
Last.fm
Diagram showing relationships among concepts
formalism. Topic maps: Both concept maps and topic maps are kinds of knowledge graph, but topic maps were developed by information management professionals for
Concept_map
Dominican-American baseball player (born 1980)
"Major League Leaderboards » 2016 » Batters » Advanced Statistics - FanGraphs Baseball". fangraphs.com. Archived from the original on December 22, 2018
Albert_Pujols
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
False or misleading information presented as real
results are "RIGGED" to mostly show only negative stories about him." They graphed his expanding use in columns labeled: "Fake news", "Fake (other) and "Phony"
Fake_news
Jewish ethnic group
Frank Harary – mathematician, widely recognized as the father of modern graph theory Shiri Maimon – singer Salha "Mama" Bobo – businesswoman, philanthropist
Syrian_Jews
January 9, 2017. Hoffman, Chris (August 2, 2016). "What's New in Windows 10s Anniversary Update". How-to-geek. Retrieved January 9, 2017. Hoffman, Chris (April
Microsoft Windows version history
Microsoft_Windows_version_history
American baseball player (born 1980)
Birdos. Retrieved March 15, 2015. "Matt Holliday - Stats - Batting | FanGraphs Baseball". www.fangraphs.com. Retrieved June 27, 2023. Miklasz, Bernie (February
Matt_Holliday
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
Electors of the U.S. president and vice president
magnifies the power of white voters". Vox. Retrieved February 1, 2021. Hoffman, Matthew M. (1996). "The Illegitimate President: Minority Vote Dilution
United States Electoral College
United_States_Electoral_College
American politician (born 1967)
of the Applied Statistics Center at Columbia University, described the graph as a "truly immoral bit of graphical manipulation." In January 2010, Chaffetz
Jason_Chaffetz
Practice of inhaling a burnt substance for psychoactive effects
Navy". www.royalnavy.mod.uk. Retrieved 29 March 2026. Jahnke, Sara A.; Hoffman, Kevin M.; Haddock, C. Keith; Long, Mark A. D.; Williams, Larry N.; Lando
Smoking
American baseball player (born 1968)
Paul (May 17, 2013). "The 1998 Astros were pretty good at hitting". FanGraphs. Retrieved February 16, 2016. Newhan, Ross (October 5, 1998). "Once again
Jeff_Bagwell
Termination of a species' lineage
(link) Freiwald, André; Lavaleye, Marc; Heugten, Bart Van; Beuck, Lydia; Hoffman, Leon (4 June 2019). "Last snails standing since the Early Pleistocene
Extinction
Graph of how much of something a consumer would buy at a certain price
A demand curve is a graph depicting the inverse demand function, a relationship between the price of a certain commodity (the y-axis) and the quantity
Demand_curve
Italian businessman (born 1976)
from the original (PDF) on 16 October 2017. Retrieved 24 February 2023. Hoffman, Reid (2018). "John Elkann: How to build a company to last". Masters of
John_Elkann
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
Combinatorial optimization problem
describing the problem using graph theory: The assignment problem consists of finding, in a weighted bipartite graph, a matching of maximum size, in
Assignment_problem
Dominican baseball player (born 1994)
February 4, 2016. Nguyen, Joe (June 28, 2016). "Rockies prospects Jeff Hoffman, Raimel Tapia named to All-Star Futures Game". The Denver Post. Retrieved
Raimel_Tapia
Branch of pragmatic philosophy
Charles Sanders Peirce bibliography Entitative graph Existential graph Hypostatic abstraction Inquiry Logical graph Philosophy of mathematics Philosophy of science
Pragmaticism
arithmetic, ratios, and percentages), topics needed for algebra (powers, roots, graphing, order of operations, variables, expressions, and scientific notation)
Mathematics education in the United States
Mathematics_education_in_the_United_States
Clustering methods
Honor of Professor S. Bochner. Donath, William; Hoffman, Alan (1972). "Algorithms for partitioning of graphs and computer logic based on eigenvectors of connections
Spectral_clustering
Tor onion service of Facebook
(October 31, 2014). "Making Connections to Facebook more Secure". Protect the Graph. Facebook. Retrieved December 4, 2014. Lemos, Robert (October 31, 2014)
Facebook_onion_address
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split
Planar_separator_theorem
on 24 December 2020 that the party would not run in the election. This graph shows the polling trends from the 2 March 2020 Israeli legislative election
2021 Israeli legislative election
2021_Israeli_legislative_election
Orchestral work by Iannis Xenakis
graphic notation looking more like a blueprint than a musical score, showing graphs of mass motion and glissandi like structural beams of the piece, with pitch
Metastaseis_(Xenakis)
biological entities. For instance, characteristics such as: sequences, graphs, geometric information, scalar and vector fields, patterns, constraints
Biological_data
Social networking service owned by Meta Platforms
that "Facebook was surprised we were able to suck out the whole social graph, but they didn't stop us once they realised that was what we were doing"
Combat that takes place in outer space
Space. Lanham, Maryland: Lexington Books. pp. 140–141. ISBN 0-7391-0713-5. Hoffman, David (2009). The Dead Hand. New York, New York: DoubleDay. pp. 71.
Space_warfare
System of health insurance
of the German population covered by public and private insurance. Their graph is reproduced below as Figure 1: German Population Enrolled in Health Insurance
National_health_insurance
pp. 144-155, IEEE Press. J. Koehler, B. Nebel, J. Hoffman and Y. Dimopoulos. Extending planning graphs to an ADL subset. Lecture Notes in Computer Science
Graphical user interface testing
Graphical_user_interface_testing
Canadian baseball player (born 1983)
Giants. On September 18, 2006, Martin hit a solo home run off of Trevor Hoffman, the third of four consecutive home runs in the bottom of the 9th inning
Russell_Martin_(baseball)
Digital video coder/decoder
Web Streaming? (2021 Update)". Dacast. 2021-06-18. Retrieved 2022-02-11. Hoffman, P. (June 2011). Requirements for Internet-Draft Tracking by the IETF Community
Video_codec
Genomic analysis technique
topologically associating domains with ultra-low resolution Hi-C data by graph structural entropy". Nature Communications. 9 (1): 3265. Bibcode:2018NatCo
Hi-C (genomic analysis technique)
Hi-C_(genomic_analysis_technique)
Federal electoral district in Alberta, Canada
Graph of election results in Lethbridge (1914-1977), Lethbridge—Foothills, Lethbridge (1987-present) (minor parties that never got 2% of the vote or didn't
Lethbridge (federal electoral district)
Lethbridge_(federal_electoral_district)
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
Dutch professional baseball league
(September 1, 2011). "Honkbal! Netherlands Bids to Host MLB in 2014". FanGraphs. Retrieved 2011-09-03. "2008 Netherlands Baseball All-Star Team and MVP"
Honkbal_Hoofdklasse
Fringe theory that Christopher Marlowe was the real author of William Shakespeare's works
perhaps the two most influential being those by Calvin Hoffman (1955) and A.D. Wraight (1994). Hoffman's main argument centred on similarities between the
Marlovian theory of Shakespeare authorship
Marlovian_theory_of_Shakespeare_authorship
View that mind is a ubiquitous feature of reality
cognitive scientist Donald D. Hoffman published The Case Against Reality: How evolution hid the truth from our eyes. Hoffman argues that consensus reality
Panpsychism
Group that provides security feedback
can be used to create and modify graph databases. Any type of administrator account is valuable to place in the graph database, including administrators
Red_team
American musical duo
and Garfunkel assumed the name Tom & Jerry; Garfunkel named himself Tom Graph, a reference to his interest in mathematics, and Simon named himself Jerry
Simon_&_Garfunkel
Isometric subgraph of a hypercube
In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph
Partial_cube
Software for working with quantitative decision models
determines a correct and efficient execution sequence using the dependency graph. It is a referentially transparent functional language, in that execution
Analytica_(software)
Japanese actor & voice actor
(General) Full Metal Panic!: The Second Raid (2005) (Middle-aged doctor) Speed Grapher (2005) (Professor) Super Robot Wars Original Generation: Divine Wars (2006)
Jin_Urayama
Branch of geometry
} . Its projection to M × R {\displaystyle M\times \mathbb {R} } is the graph of the function. This also shows that J 1 ( M , R ) {\displaystyle J^{1}(M
Contact_geometry
Capital city of Virginia, United States
was on October 30 and the average last one on April 10. See or edit raw graph data. Richmond's population is approximately 226,000. As an independent
Richmond,_Virginia
English-language edition of Wikipedia
Archived from the original on 17 September 2020. Retrieved 9 June 2009. Hoffman, David A.; Salil Mehra (2010). "Wikitruth Through Wikiorder". Emory Law
English_Wikipedia
Unsolved problem in graph theory
mathematics For which 2-regular n {\displaystyle n} -vertex graphs G {\displaystyle G} can the complete graph K n {\displaystyle K_{n}} be decomposed into edge-disjoint
Oberwolfach_problem
Brazilian internet entrepreneur (born 1982)
Archived from the original on October 6, 2018. Retrieved March 28, 2017. Hoffman, Claire (September 15, 2010). "The Battle For Facebook". Rolling Stone
Eduardo_Saverin
Use of an excessive amount of a drug
sexes. Run your cursor over the graph to see the data. Nelson, Lewis H.; Flomenbaum, Neal; Goldfrank, Lewis R.; Hoffman, Robert Louis; Howland, Mary Deems;
Drug_overdose
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
Major League Baseball team season
Sports. March 30, 2023. Retrieved September 30, 2023. "MLB Playoff Odds". FanGraphs. March 29, 2023. Retrieved September 30, 2023. "MLB season preview: Rankings
2023_San_Diego_Padres_season
American computer scientist (born 1976)
search engine. In it she invented an early approach to using the web link graph to support information seeking. Teevan also received a Ph.D. and S.M. from
Jaime_Teevan
County in Kentucky, United States
"Warren County, Kentucky - Kentucky Atlas and Gazetteer". www.uky.edu. Hoffman, Dr. Wayne (1989). "The History of Bowling Green and Warren County" (PDF)
Warren_County,_Kentucky
1998 mathematics book by Aigner and Ziegler
number of Kneser graphs. Chapter 44: Friendship theorem. Chapter 45: Some proofs using the probabilistic method. Klarreich (2018). Hoffman (1999), p. 26
Proofs_from_THE_BOOK
Image and video hosting website
Graph of Flickr public uploads, which peaked in 2013–2015 before the launch of Google Photos
Flickr
Probabilistic graphical representation of causal relationships
of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks
Bayesian_network
National Hockey League team season
on June 10, 1981. 1981–82 NHL season "Hartford Whalers Yearly Attendance Graph". hockeydb.com. Dinger, Ralph, ed. (2011). The National Hockey League Official
1981–82 Hartford Whalers season
1981–82_Hartford_Whalers_season
Thornton Giancarlo Bigazzi Raffaele Riefoli Stephen Piccolo "Champion" feat. Graph Nobel Gene Thornton Terrence Thornton "Life Change" feat. Kenna Gene Thornton
Pharrell Williams production discography
Pharrell_Williams_production_discography
American multinational technology company
The Wall Street Journal. Retrieved January 14, 2022. "Five year history graph of (NASDAQ:MSFT) stock". ZenoBank. AlphaTrade. September 29, 2009. Archived
Microsoft
Greek-owned cargo ship sunk in WW2, & survivors massacred
guilty. Eck was sentenced to death, as was his second in command August Hoffman, and his ship's doctor. They were executed by firing squad on 30 November
SS_Peleus
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