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Construction in graph theory
In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation
McKay_graph
In graph theory, the McKay–Miller–Širáň graphs are an infinite class of vertex-transitive graphs with diameter two, and with a large number of vertices
McKay–Miller–Širáň_graph
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Australian mathematician (born 1951)
in 2000. McKay is the author of at least 127 refereed articles. One of McKay's main contributions has been a practical algorithm for the graph isomorphism
Brendan_McKay_(mathematician)
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
Delorme & Farhi (1982). McKay–Miller–Širáň graphs found by McKay, Miller & Širáň (1998). Graph found by Vlad Pelakhaty in 2021. Graphs found by Gómez, Fiol
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
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Brendan McKay and Nicholas Wormald. Béla Bollobás, Random Graphs, 2nd edition, Cambridge University Press (2001), section 2.4: Random Regular Graphs Bollobás
Random_regular_graph
Faulkner and Younger published two more graphs – the Faulkner–Younger graphs on 42 and 44 vertices. Finally Holton and McKay showed there are exactly six 38-vertex
Tutte_graph
Unsolved problem in computational complexity theory
graphs was obtained by Babai & Codenotti (2008). There are several competing practical algorithms for graph isomorphism, such as those due to McKay (1981)
Graph_isomorphism_problem
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Mathematical classification
described in (Dickson 2004). The correspondence uses the construction of McKay graph. Note that the ADE correspondence is not the correspondence of Platonic
ADE_classification
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Constructs with triply-connected vertices
connected 3-regular (cubic) simple graphs are listed for small vertex numbers. The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is
Table_of_simple_cubic_graphs
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
Statement in mathematical combinatorics
colouring of the graph KL−1 with no blue Kr subgraph and no red Ks subgraph. Such a counterexample is called a Ramsey graph. Brendan McKay maintains a list
Ramsey's_theorem
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and
Rooted_graph
Disproven graph theory
McKay (1988). The condition that the graph be 3-regular is necessary due to polyhedra such as the rhombic dodecahedron, which forms a bipartite graph
Tait's_conjecture
Type of graph vertex labeling
graceful labeling? More unsolved problems in mathematics In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some
Graceful_labeling
Task in computational graph theory
York, pp. 153–182, MR 0344150. McKay, Brendan D.; Piperno, Adolfo (2014), "Journal of Symbolic Computation", Practical graph isomorphism, II, vol. 60, pp
Graph_canonization
Graph in climate science
Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions
Hockey stick graph (global temperature)
Hockey_stick_graph_(global_temperature)
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
Conjecture in graph theory
for all graphs with at most 13 vertices by Brendan McKay. In a probabilistic sense, it has been shown by Béla Bollobás that almost all graphs are reconstructible
Reconstruction_conjecture
Second-smallest eigenvalue of a graph Laplacian
and in fact (in a result due to Brendan McKay) by 4 n D {\textstyle {\frac {4}{nD}}} . For the example graph with 6 nodes show above ( n = 6 , D = 3 {\textstyle
Algebraic_connectivity
Graph where every edge is in one triangle
In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the
Locally_linear_graph
testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that cannot be
Colour_refinement_algorithm
Unsolved problem in graph theory
Aldred, R. E. L.; Bau, S.; Holton, D. A.; McKay, Brendan D. (2000), "Nonhamiltonian 3-connected cubic planar graphs", SIAM Journal on Discrete Mathematics
Barnette's_conjecture
Non-Hamiltonian simple polyhedron
non-Hamiltonian polyhedral graphs are possible, including the Goldner–Harary graph and the Herschel graph. Holton, D. A.; McKay, B. D. (1988), "The smallest
Barnette–Bosák–Lederberg graph
Barnette–Bosák–Lederberg_graph
Use of mathematical groups in magnetochemistry
species CH3F+ and CH3BF2+ which both contain a single unpaired electron. McKay graph ADE classification Molecular symmetry Point group Space group In his
Finite_subgroups_of_SU(2)
Formula used in graph theory
LSE-CDAM-2004-12, 2004. Brendan McKay and Robert W. Robinson, Asymptotic enumeration of eulerian circuits in the complete graph, Combinatorica, 10 (1995),
BEST_theorem
hypohamiltonian graphs", Journal of Graph Theory, 67 (1): 55–68, doi:10.1002/jgt.20513, MR 2809563, S2CID 5340663. Jooyandeh, Mohammadreza; McKay, Brendan D
Wiener–Araya_graph
Type of graph in graph theory
mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing
Hypohamiltonian_graph
Mathematical Graph
In graph theory, a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself
Walk-regular_graph
Binary operation performed on graphs
In mathematical graph theory, the rooted product (or comb product) of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and
Rooted_product_of_graphs
Software for visualizing chemical structures
A chemical graph generator is a software package to generate computer representations of chemical structures adhering to certain boundary conditions.
Chemical_graph_generator
British-canadian mathematician
Hyman Soicher is a British-Canadian mathematician who worked in algebraic graph theory, group theory, combinatorial design theory, and discrete computational
Leonard_Soicher
Mike Gregory, English darts player (b. 1956). John McKay, mathematician (McKay conjecture, McKay graph) (b. 1939). Henry Scott-Stokes, journalist (Financial
2022 deaths in the United Kingdom
2022_deaths_in_the_United_Kingdom
Mathematical problem set on a chessboard
problem is an instance of the more general Hamiltonian path problem in graph theory. The problem of finding a closed knight's tour is similarly an instance
Knight's_tour
(2001), Algebraic Graph Theory, Graduate Texts in Math., Vol. 207, Springer-Verlag, New York. Brendan McKay (1981), Practical graph isomorphism, Congressus
Equitable_partition
Planar maps require at most four colors
blocks in 3-space", Discussiones Mathematicae Graph Theory, 31 (1): 161–170, doi:10.7151/dmgt.1535 McKay, Brendan D. (2012), A note on the history of the
Four_color_theorem
Australian mathematician
Australia. Royle is the co-author (with Chris Godsil) of the book Algebraic Graph Theory (Springer Verlag, 2001, ISBN 0-387-95220-9). Royle is also known
Gordon_Royle
Polytope
stochastic matrices, or the perfect matching polytope of the complete bipartite graph K n , n {\displaystyle K_{n,n}} . The Birkhoff polytope has n ! {\displaystyle
Birkhoff_polytope
In mathematics, a fibration of graphs, or graph fibration, is a homomorphism of directed graphs that satisfies a unique lifting property analogous to that
Fibrations_of_graphs
Canadian flight attendant and early AIDS victim (1952–1984)
consistent with the hypothesis that AIDS was caused by an infectious agent. A graph included with the paper traced the sequence of infection among 40 men, and
Gaëtan_Dugas
28 lines which touch a general quartic plane curve in two places
Manivel (2006). Dejter, Italo J. (2011), "From the Coxeter graph to the Klein graph", Journal of Graph Theory, 70: 1–9, arXiv:1002.1960, doi:10.1002/jgt.20597
Bitangents_of_a_quartic
Pictorial representation of symmetry
of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin
Dynkin_diagram
Measure of centrality in a network based on nodal influence
In graph theory, the Katz centrality or alpha centrality of a node is a measure of centrality in a network. It was introduced by Leo Katz in 1953 and
Katz_centrality
Olympic bronze medallist (1956). John McKay, 82, British-Canadian mathematician (McKay conjecture, McKay graph). Ardina Moore, 91, American Quapaw-Osage
Deaths_in_April_2022
Czech-Australian mathematician and computer scientist
vertex-transitive graphs with diameter two and a large number of vertices relative to their degree and diameter, the McKay–Miller–Širáň graphs, are named after
Mirka_Miller
Australian mathematician
Retrieved 25 May 2013. Brendan D McKay; Nicholas C Wormald (1991). "Asymptotic enumeration by degree sequence of graphs with degrees o ( n ½ ) " (PDF).
Nick_Wormald
Measure in graph theory
In graph theory, eigenvector centrality (also called eigencentrality or prestige score) is a measure of the influence of a node in a connected network
Eigenvector_centrality
3-regular graph
The uniqueness was proved by Brendan McKay and Wendy Myrvold in 2003. The Balaban 11-cage is a Hamiltonian graph and can be constructed by excision from
Balaban_11-cage
Algorithm used by Google Search to rank web pages
The PageRank of an undirected graph G {\displaystyle G} is statistically close to the degree distribution of the graph G {\displaystyle G} , but they
PageRank
Type of sports competition
table. The above schedule can also be represented by a graph, as shown below: Both the graph and the schedule were reported by Édouard Lucas in as a
Round-robin_tournament
Sporadic simple group
multiplier has order 6. The Fischer group Fi22 has a rank 3 action on a graph of 3510 vertices corresponding to its 3-transpositions, with point stabilizer
Fischer_group_Fi22
New Zealand mathematician
specialising in combinatorics, including the theories of Latin squares and random graphs. She is a senior lecturer in the School of Mathematics and Statistics at
Jeanette_McLeod
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"
Natural number
a primitive semiperfect number. The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at
104_(number)
Method to convey chess moves
Chess. Burgess, Graham (2000) [1997]. The Mammoth Book of Chess. Carroll & Graph. p. 517. ISBN 0-7867-0725-9. Article 9.1.2.2 in FIDE Laws of Chess User's
Algebraic_notation_(chess)
Sporadic simple group
group J2. It happens that J2 acts as a permutation group on the Hall–Janko graph of 100 points, the stabilizer of one point being a subgroup with two other
Higman–Sims_group
Sporadic simple group
Society. 49 (9) – via ams.org. le Bruyn, Lieven (22 April 2009). "The monster graph and McKay's observation". neverendingbooks. Conway, J.H. (1985). "A simple
Monster_group
(generated by a Frobenius automorphism), and g is the order of the group of "graph automorphisms" (coming from automorphisms of the Dynkin diagram). The outer
List_of_finite_simple_groups
Assembly of systems connected to manage forces and movement
chain can be modeled as a graph in which the links are paths and the joints are vertices, which is called a linkage graph. The movement of an ideal joint
Linkage_(mechanical)
1997 book by Michael Drosnin
passages at equal intervals in a text that has been formatted to fit inside a graph. Drosnin suggests that the code was written by extraterrestrial life (which
The_Bible_Code_(book)
Polish-American mathematician and computer scientist
many papers in graph theory, Ramsey theory, block designs, number theory and computational complexity. In a 1995 paper with Brendan McKay he determined
Stanisław_Radziszowski
Polyhedron associated with another by swapping vertices for faces
Polyhedra, based on paper by Gunnar Brinkmann, Brendan D. McKay, Fast generation of planar graphs PDF [1] Anthony M. Cutler and Egon Schulte; "Regular Polyhedra
Dual_polyhedron
Mathematical problem
MOLS(n) is equivalent to an edge-partition of the complete (k + 2)-partite graph Kn,...,n into complete subgraphs of order k + 2. Mutually orthogonal Latin
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Method of describing higher-order polyhedra
equivalent polyhedra can be thought of as one of many embeddings of a polyhedral graph on the sphere. Unless otherwise specified, in this article (and in the literature
Conway_polyhedron_notation
Marijuana Hits Record 70%". Gallup.com. Gallup, Inc. Data link is at bottom of graph. State-By-State Medical Marijuana Laws (PDF), Marijuana Policy Project,
Legality of cannabis by U.S. jurisdiction
Legality_of_cannabis_by_U.S._jurisdiction
Sporadic simple group
group are both trivial. The Fischer group Fi23 has a rank 3 action on a graph of 31671 vertices corresponding to 3-transpositions, with point stabilizer
Fischer_group_Fi23
Tool for a fast finite-field arithmetic
one obtains a graph G α ( q ; c ) {\displaystyle G_{\alpha }(q;c)} . The standard graph corresponds to c = 1 {\displaystyle c=1} . The graph G α ( q ; 0
Zech's_logarithm
October 27, 2021.{{cite news}}: CS1 maint: deprecated archival service (link) McKay, Dan (April 17, 2021). "Republican Commissioner Jay Block enters governor's
2022 New Mexico gubernatorial election
2022_New_Mexico_gubernatorial_election
Mathematical transformation
negative of the y {\displaystyle y} -intercept of the tangent line to the graph of f {\displaystyle f} that has slope p {\displaystyle p} . The generalization
Legendre_transformation
Steps in reasoning
metalanguagePages displaying short descriptions of redirect targets Logical graph – Type of diagrammatic notation for propositional logicPages displaying
Inference
Earth's southernmost continent
most recent charted data by a few months.) "Charctic Interactive Sea Ice Graph: A Sea Ice Today Tool". National Snow and Ice Data Center. University of
Antarctica
Chess piece
queen+knight compound piece Eight queens puzzle Queen versus pawn endgame Queen's graph Staunton chess set Larsen, Bent (1975), Lærebok i sjakk "Nakamura's 2.Qh5"
Queen_(chess)
Artificial intelligence division of Meta Platforms
2017. Archived from the original on May 8, 2022. Retrieved May 8, 2022. McKay, Tom (August 1, 2017). "No, Facebook Did Not Panic and Shut Down an AI Program
Meta_Superintelligence_Labs
This graph was using the legacy Graph extension, which is no longer supported. It needs to be converted to the new Chart extension.
2020 United States Senate election in Alaska
2020_United_States_Senate_election_in_Alaska
Bilateral relations
Archived from the original on December 27, 2021. Retrieved April 13, 2024. McKay, Hollie (June 17, 2020). "Jeffrey Epstein's alleged 'spy' ties under fresh
Israel–United States relations
Israel–United_States_relations
Type of sub-graph
PMID 16020473. McKay BD (1981). "Practical graph isomorphism". Congressus Numerantium. 30: 45–87. arXiv:1301.1493. Bibcode:2013arXiv1301.1493M. McKay BD (1998)
Network_motif
Australian mathematician
Australia. His research area is combinatorics, principally Latin squares, graph theory and matrix permanents. Wanless completed his secondary education
Ian_Wanless
Square array with symbols that each occur once per row and column
square in 1700, predating Leonhard Euler by 67 years. This account follows McKay, Meynert & Myrvold (2007, p. 100). The counting of Latin squares has a long
Latin_square
Earth's southern polar ice cap
Elie Verleyen; Philip E. O'Brien; Duanne A. White; R. Selwyn Jones; Robert McKay; Robert Dunbar; Damian B. Gore; David Fink; Alexandra L. Post; Hideki Miura;
Antarctic_ice_sheet
Hypothetical relationship between development and inequality
intensity Kuznets Curve" were by Huw McKay in a 2008 working paper (McKay 2008). This was subsequently developed by McKay (2012). A body of work on "Material
Kuznets_curve
Federal electoral district in Ontario, Canada
Graph of election results in Thunder Bay—Superior North (minor parties that never got 2% of the vote or didn't run consistently are omitted)
Thunder Bay—Superior North (federal electoral district)
Thunder_Bay—Superior_North_(federal_electoral_district)
Sporadic simple group
field with 3 elements. The simple Fischer group has a rank 3 action on a graph of 306936 (=23.33.72.29) vertices corresponding to the 3-transpositions
Fischer_group_Fi24
U.S. state
Graph of Oregon's population growth from 1850 to 2010
Oregon
Federal electoral district in Alberta, Canada
Graph of election results in Edmonton West (since 2015, minor parties that never got 2% of the vote or didn't run consistently are omitted)
Edmonton_West
One of the two categories of Indigenous Australians
ISSN 2770-5005. Mallick et al. found that a well-fitting admixture graph (qpGraph, Box 1) grouped Papuans, Australians, and the Andamanese Onge with East
Aboriginal_Australians
Federal electoral district in Alberta, Canada
Graph of election results in Fort McMurray—Cold Lake (minor parties that never got 2% of the vote or didn't run consistently are omitted)
Fort_McMurray—Cold_Lake
Type of regression analysis
symbolic regression exploiting graph modularity". arXiv:2006.10782 [cs.LG]. Mark J. Willis; Hugo G. Hiden; Ben McKay; Gary A. Montague; Peter Marenbach
Symbolic_regression
City in Nevada, United States
snowfall in a calendar year was 82.3 inches (209 cm) in 1916. See or edit raw graph data. As of the census of 2010, there were 225,221 people, 90,924 households
Reno,_Nevada
Graph of opinion polls conducted in Scotland
2024 United Kingdom general election in Scotland
2024_United_Kingdom_general_election_in_Scotland
Provincial party election in Alberta, Canada
Billy Morin (Chief of Enoch Cree Nation) Ron Quintal (President of Fort McKay Métis Nation) Former MLAs: (2) David Dorward (MLA for Edmonton-Gold Bar
2022 United Conservative Party leadership election
2022_United_Conservative_Party_leadership_election
Indian cricketer (born 1973)
target, he tried to scoop a slower delivery from debutant bowler Clint McKay over short fine leg only to be caught by Nathan Hauritz, with India needing
Sachin_Tendulkar
Graphical tool in probability
truncated vines and cherry tree copulas is presented in ( ) Cherry tree graph representations were introduced as an alternative for the usual graphical
Vine_copula
made a total of five flights. JPL · 8025 8026 Johnmckay 1991 JA1 John B. McKay (1922–1975), a NASA research pilot who was the 5th pilot to fly the X-15
Meanings of minor-planet names: 8001–9000
Meanings_of_minor-planet_names:_8001–9000
Federal electoral district in Ontario, Canada
Graph of election results in Scarborough—Guildwood since 2004 (parties that never received at least 2% of the vote are omitted)
Scarborough—Guildwood (federal electoral district)
Scarborough—Guildwood_(federal_electoral_district)
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