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Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
Type of graph in graph theory
of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is
Half-transitive_graph
Mapping a graph onto itself without changing edge-vertex connectivity
graph is a graph that is edge-transitive but not vertex-transitive. A half-transitive graph is a graph that is vertex-transitive and edge-transitive but
Graph_automorphism
graph is transitively closed if it equals its own transitive closure; see transitive. 4. A graph property is closed under some operation on graphs if
Glossary_of_graph_theory
In graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive
Holt_graph
Class of undirected graphs defined from systems of sets
is a k × ( n − k ) {\displaystyle k\times (n-k)} rook's graph. There is a distance-transitive subgroup of Aut ( J ( n , k ) ) {\displaystyle \operatorname
Johnson_graph
One of two different regular graphs with 16 vertices
Cayley graph, its automorphism group acts transitively on its vertices, making it vertex transitive. In fact, it is arc transitive, hence edge transitive and
Clebsch_graph
Cubic graph with 8 vertices and 12 edges
with the same number of vertices. The Wagner graph is a vertex-transitive graph but is not edge-transitive. Its full automorphism group is isomorphic to
Wagner_graph
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
Area of discrete mathematics
of graphs based on symmetry in algebraic graph theory. Such a symmetry includes symmetric graphs, vertex-transitive graphs, edge-transitive graphs, distance-transitive
Graph_theory
Graph representing edges of another graph
number of a graph G is equal to the vertex chromatic number of its line graph L(G). The line graph of an edge-transitive graph is vertex-transitive. This property
Line_graph
Two special graphs in graph theory
group acts transitively on its half-edges, so the Klein graph is a symmetric graph. The characteristic polynomial of this 56-vertex Klein graph is equal
Klein_graphs
24-vertex symmetric bipartite cubic graph
census, the Nauru graph is the only cubic symmetric graph on 24 vertices. The generalized Petersen graph G(n,k) is vertex-transitive if and only if n = 10
Nauru_graph
Symmetric bipartite cubic graph with 16 vertices and 24 edges
Möbius–Kantor graph is the unique cubic symmetric graph with 16 vertices, and the smallest cubic symmetric graph which is not also distance-transitive. The Möbius–Kantor
Möbius–Kantor_graph
Bipartite 4-regular graph with 20 nodes and 40 edges
smallest undirected graph that is edge-transitive and regular, but not vertex-transitive. Such graphs are called semi-symmetric graphs and were first studied
Folkman_graph
Slovenian mathematician
vertex-transitive graphs, the existence of Hamiltonian paths and cycles in vertex-transitive graphs, and the structures of semi-symmetric graphs and half-transitive
Dragan_Marušič
Mathematical set with an ordering
is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X
Partially_ordered_set
Flat-sided three-dimensional shape
vertex-transitive and edge-transitive is said to be quasiregular; they have regular faces, and their duals are face-transitive and edge-transitive. A vertex-
Polyhedron
Structure-preserving correspondence between node-link graphs
the relation → on graphs is transitive (and reflexive, trivially), so it is a preorder on graphs. Let the equivalence class of a graph G under homomorphic
Graph_homomorphism
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
Catalan solid with 12 faces
symmetry, the octahedral symmetry. It is face-transitive, meaning the symmetry group of the solid acts transitively on its set of faces. In elementary terms
Rhombic_dodecahedron
Polyhedron with 8 triangles and 6 squares
elements colored by transitivity positions. The graph of a cuboctahedron may be constructed as the line graph of the cubical graph, making it becomes the
Cuboctahedron
Solid with six equal square faces
drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube
Cube
Representation of cubic graphs
Kutnar, Klavdija; Marušič, Dragan (2008), "Hamiltonicity of vertex-transitive graphs of order 4p", European Journal of Combinatorics, 29 (2): 423–438,
LCF_notation
Bipartite 3-regular graph with 90 vertices and 135 edges
are known. The Foster graph is one of the 13 such graphs. It is the unique distance-transitive graph with intersection array {3,2,2,2,2,1,1,1;1,1,1,1,2
Foster_graph
Undirected graph derived from a hypercube graph
In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs
Folded_cube_graph
Upper bound on a graph's Shannon capacity
In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász
Lovász_number
Task of computing complete subgraphs
463–470. Even, S.; Pnueli, A.; Lempel, A. (1972), "Permutation graphs and transitive graphs", Journal of the ACM, 19 (3): 400–410, doi:10.1145/321707.321710
Clique_problem
Network whose degree distribution follows a power law
transformation which converts random graphs to their edge-dual graphs (or line graphs) produces an ensemble of graphs with nearly the same degree distribution
Scale-free_network
Archimedean solid with 26 faces
rhombicuboctahedron, but it is not an Archimedean solid because it is not vertex-transitive. The rhombicuboctahedron is found in diverse cultures in architecture
Rhombicuboctahedron
directed graph Johnson's algorithm: all pairs shortest path algorithm in sparse weighted directed graph Transitive closure problem: find the transitive closure
List_of_algorithms
Directed graph isomorphic to its own transpose graph
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by
Skew-symmetric_graph
Tessellation of convex uniform polyhedron cells
honeycombs, 11 are regular, meaning that their group of symmetries acts transitively on their flags. These have Schläfli symbol {3,3,6}, {6,3,3}, {3,4,4}
Paracompact uniform honeycombs
Paracompact_uniform_honeycombs
Archimedean solid with 14 faces
so that its sliced cross-section is a truncated octahedron. The cell-transitive bitruncated cubic honeycomb can also be seen as the Voronoi tessellation
Truncated_octahedron
Problem in computer networking
are exploited for their mobility. Since they are the primary source of transitive communication between two non-neighboring nodes in the network, an important
Routing in delay-tolerant networking
Routing_in_delay-tolerant_networking
Game variations and descriptions of intransitive dice and their behaviour
higher number than Y more than half the time – on its elements is not transitive. More simply, X 1 {\displaystyle X_{1}} normally beats X 2 {\displaystyle
Intransitive_dice
Alternative mathematical ordering
set with a free transitive action by a finite cyclic group. Another formulation is to make X into the standard directed cycle graph on n vertices, by
Cyclic_order
Four finite groups derived from the Leech lattice
|Λ2| = 196,560 = 24⋅33⋅5⋅7⋅13. Conway strongly suspected that Co0 was transitive on Λ2, and indeed he found a new matrix, not monomial and not an integer
Conway_group
Polyhedron with 12 faces
same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular:
Dodecahedron
Argentine-born American mathematician
undirected, bipartite graph with 112 vertices and 168 edges, (semi-symmetric, that is edge-transitive but not vertex-transitive, cubic graph with diameter 8
Italo_Jose_Dejter
Isometric subgraph of a hypercube
reflexive and symmetric, but in general it is not transitive. Winkler showed that a connected graph is a partial cube if and only if it is bipartite and
Partial_cube
Isogonal polyhedron with regular faces
and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if neither edge- nor face-transitive). The faces
Uniform_polyhedron
Symmetric subdivision in hyperbolic geometry
face- and edge-transitive), quasi-regular (if edge-transitive but not face-transitive) or semi-regular (if neither edge- nor face-transitive). For right
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Clustering and community detection algorithm
that every community has two nodes. In this case, aggregateGraph would return a graph half the size of the original. If this continued, then the Louvain
Louvain_method
Algorithm used by Google Search to rank web pages
group called Contact Youth. SD2 uses PageRank for the processing of the transitive proxy votes, with the additional constraints of mandating at least two
PageRank
Type of computational problem
f(x_{A})} have the same number of solutions. This reduction is reflexive and transitive. Some problems are ♯P-complete under polynomial-time parsimonious counting
Counting_problem_(complexity)
Geometric configuration of 9 points and 12 lines
4\\3&12\\\end{smallmatrix}}\right]} . It is symmetric (point and line transitive) with 432 automorphisms. It can be realized in the complex projective
Hesse_configuration
Logic problem, AND of pairwise ORs
implication graph of the 2-satisfiability instance, Krom's inference rule can be interpreted as constructing the transitive closure of the graph. As Cook
2-satisfiability
professionals "blockers". The word derives from the slightly archaic transitive verb, "biff" which means "hit". Today, biffers tend to be known as big
Glossary_of_cricket_terms
Shape in hyperbolic geometry
is met: either the graph of the polyhedron is a bipartite graph and its dual graph is 4-connected, or it is a 1-supertough graph. In this condition,
Ideal_polyhedron
Self-intersecting polyhedron with 12 faces
solids meet at each vertex. This honeycomb is cell-transitive, edge-transitive and vertex-transitive. The Yoshimoto Cube, a dissection puzzle between a
First stellation of the rhombic dodecahedron
First_stellation_of_the_rhombic_dodecahedron
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
Family of random graph models
specified for different types of graphs: Simple graphs: Graphs without self-loops or multi-edges. Multi-edge graphs: Graphs allowing multiple edges between
Configuration_model
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)
prismatorhombisnub icositetrachoron, s3{3,4,3}, . It is not uniform, but it is vertex-transitive and has all regular polygon faces. It is constructed with 24 icosahedra
Runcinated_24-cells
Uniqueness of countable dense linear orders
that gives an ordering to each pair of distinct elements and obeys the transitive law. The familiar numeric orderings on the integers, rational numbers
Cantor's_isomorphism_theorem
Construction in group theory
2), or is half this (if the characteristic is not 2). The action of the projective linear group on the projective line is sharply 3-transitive (faithful
Projective_linear_group
Field of mathematics dealing with three-dimensional Euclidean spaces
convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube Some sources also require that each of the
Solid_geometry
Human contact that exists because of a mutual friend
is not automatically a transitive relation produces some social dynamics. In some social sciences, the phrase is used as a half-joking shorthand for the
Friend_of_a_friend
Probabilistic Condorcet method
{\displaystyle q} than vice versa. While this relation is not necessarily transitive, it does always admit at least one maximal element. It is possible that
Maximal_lotteries
Aesthetic quality of blur in the out-of-focus parts of an image
(暈かし) means intentional blurring or gradation; that is a noun form of the transitive verb bokasu (暈す), which means to make something blurry, rather than to
Bokeh
Eastern Iranian language of Ossetia, in the Caucasus
д- d-, ст- st- оr in a vowel (see below). There are also many related transitive-intransitive verb pairs, which also differ by means of a vowel alternation
Ossetian_language
Basic notion of sameness in mathematics
concept. Basic properties about equality like reflexivity, symmetry, and transitivity have been understood intuitively since at least the ancient Greeks, but
Equality_(mathematics)
Isomorphism type of ordered sets
order type denoted by ω, as explained below. The rationals contained in the half-closed intervals [0,1) and (0,1], and the closed interval [0,1], are three
Order_type
Plane figure bounded by line segments
or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular. Isotoxal or edge-transitive: all sides
Polygon
Pictorial representation of symmetry
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter
Coxeter–Dynkin_diagram
Class of 4-dimensional polytopes
4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons
Uniform_4-polytope
Arrangement of a communication network
network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections
Network_topology
polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra. It has half the vertices of a runcinated tesseract, with its construction, called a runcic
Rectified_tesseract
Uniform 4-polytope
cuboidal envelope (see diagram). Each triangular prismic cell projects onto half of the cuboidal volume, forming two pairs of overlapping images. The tetrahedral
Tetrahedral_prism
Natural number
are twelve Jacobian elliptic functions and twelve cubic distance-transitive graphs. A twelve-sided polygon is a dodecagon. In its regular form, it is
12_(number)
2x2x2 combination puzzle
same initial configuration. In addition, the relation is symmetrical and transitive, as it is similar to the mathematical relation of equality. With this
Pocket_Cube
interval on the real line that is usually considered is the closed-open right half of the real line, that is, the interval [ 0 , ∞ ) {\displaystyle [0,\infty
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Compact Riemann surface of genus 3
over infinity. The resulting dessin is a "platonic" dessin, meaning edge-transitive and "clean" (each white point has valence 2). The Klein quartic is related
Klein_quartic
1999 Microsoft operating system version
authentication system used in previous versions. This also provided a purely transitive-trust relationship between Windows 2000 Server domains in a forest (a
Windows_2000
Type of tesseract
applied to the tesseract. It can also be called a runcicantic tesseract with half the vertices of a runcicantellated tesseract with a construction. Bitruncated
Truncated_tesseract
Five-dimensional geometric shape
five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets. The complete set of convex
Uniform_5-polytope
Hand game for two players or more
relatively general evolutionary model. The general nature of this basic non-transitive model is widely applied in theoretical biology to explore bacterial ecology
Rock_paper_scissors
Covering by shapes without overlaps or gaps
hyperbolic plane, with regular polygons as faces; these are vertex-transitive (transitive on its vertices), and isogonal (there is an isometry mapping any
Tessellation
Upper bound on intersecting set families
independent set. Because Kneser graphs have symmetries taking any vertex to any other vertex (they are vertex-transitive graphs), their fractional chromatic
Erdős–Ko–Rado_theorem
Polyhedron with parallel bases connected by triangles
uniform prisms, the uniform antiprisms form an infinite class of vertex-transitive polyhedra. For n = 2, one has the digonal antiprism (degenerate antiprism)
Antiprism
Shape with six sides
alternating between two parallel planes. A regular skew hexagon is vertex-transitive with equal edge lengths. In three dimensions it will be a zig-zag skew
Hexagon
Field of mathematics and science based on non-linear systems and initial conditions
it must be sensitive to initial conditions, it must be topologically transitive, it must have dense periodic orbits. In some cases, the last two properties
Chaos_theory
Abstract mathematics problem
performed at 15 seconds before noon. Each subsequent step is performed in half the time of the previous step, i.e., step n is performed at 2−n minutes before
Ross–Littlewood_paradox
Geometric theorem
these points into a set M. The action of H on a given orbit is free and transitive and so each orbit can be identified with H (except for countably many
Banach–Tarski_paradox
Concept in economics and decision theory
preferred or that they are indifferent), and that the preference order is transitive. Suppose the set of alternatives is not finite (for example, even if the
Utility
Geometric arrangements of points, foundational to Lie theory
Finally, root systems are important for their own sake, as in spectral graph theory. As a first example, consider the six vectors in 2-dimensional Euclidean
Root_system
Generalized manifold
2-dimensional simplicial complexes with the regular action of a group, transitive on triangles. A triangle of groups is a simple complex of groups consisting
Orbifold
Uniform 6-dimensional polytope
is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform
Uniform_6-polytope
Mathematical group of the homotopy classes of loops in a topological space
\mathrm {SU} (n),} with n ≥ 2. {\displaystyle n\geq 2.} This group acts transitively on the unit sphere S 2 n − 1 {\displaystyle S^{2n-1}} inside C n = R
Fundamental_group
become generic and lacks trademark significance due to its common use as a transitive verb. After losing to Google in UDRP proceedings involving many "Google-related"
History_of_Google
Concerned with the notion of stability in model theory
in some model M such that ϕ {\displaystyle \phi } defines an infinite half graph on A × B {\displaystyle A\times B} , i.e. ϕ ( a ¯ i , b ¯ j ) {\displaystyle
Stable_theory
Natural number
11130 and 77711; number of regular simple graphs spanning 7 vertices 932 = 22 × 233, number of regular simple graphs on 7 labeled nodes 933 = 3 × 311 934 =
900_(number)
Prokopenko M, Hossain L (2013-01-22). "Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks". PLOS ONE. 8 (1)
Targeted immunization strategies
Targeted_immunization_strategies
Shape with four equal sides and angles
and, more generally, a regular polygon act transitively on vertices and edges, and simply transitively on half-edges. Combining any two of these transformations
Square
Convex polyhedron projected from hypercube
and the 1-skeleton of the zonohedron can be viewed as the planar dual graph to an arrangement of great circles on the sphere. Conversely any arrangement
Zonohedron
Integer side lengths of a right triangle
acts on the collection of all integer spinors. Furthermore, the group is transitive on the collection of integer spinors with relatively prime entries. For
Pythagorean_triple
Ordering of binary values, used for positioning and error correction
vertex-transitive graph contains a Hamiltonian path. The "middle-level" subgraph Q 2 n + 1 ( n ) {\displaystyle Q_{2n+1}(n)} is vertex-transitive (that
Gray_code
Single-winner electoral system
other candidate via a beatpath-win. This definition of a beatpath-win is transitive: in other words, if Alice has a beatpath-win over Bob, and Bob has a beatpath-win
Schulze_method
Mathematical table used in logic
Functional completeness Karnaugh maps Logic gate Logical connective Logical graph Mathematical table Method of analytic tableaux Propositional calculus Truth
Truth_table
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
Boy/Male
English Swedish Teutonic
Lives in the hall.
Boy/Male
American, Anglo, Australian, British, Christian, English, French, German, Teutonic
Ingenious; From the Hall; Healthy Hero
Male
English
Pet form of English Henry, HAL means "home-ruler."
Girl/Female
Muslim
Lunar halo. Glory.
Boy/Male
Hindu
Transition
Male
English
Short form of English Alfred, ALF means "elf counsel." Compare with other forms of Alf.
Male
English
 English surname transferred to forename use, derived from Old English heall "hall," hence "lives at the hall." Middle English name HALL means "to cover, conceal."
Boy/Male
Norse
Half son of Asgeir.
Boy/Male
Christian & English(British/American/Australian)
From the Hall or Manor
Male
Scandinavian
Scandinavian form of Old Norse Alfr, ALF means "elf." Compare with other forms of Alf.
Girl/Female
Indian
Aureole, Halo around the Moon
Surname or Lastname
English, Scottish, Irish, German, and Scandinavian
English, Scottish, Irish, German, and Scandinavian : from Middle English hall (Old English heall), Middle High German halle, Old Norse hǫll all meaning ‘hall’ (a spacious residence), hence a topographic name for someone who lived in or near a hall or an occupational name for a servant employed at a hall. In some cases it may be a habitational name from places named with this word, which in some parts of Germany and Austria in the Middle Ages also denoted a salt mine. The English name has been established in Ireland since the Middle Ages, and, according to MacLysaght, has become numerous in Ulster since the 17th century.Hall is one of the commonest and most widely distributed of English surnames, bearing witness to the importance of the hall as a feature of the medieval village.
Boy/Male
Tamil
Transition
Girl/Female
Muslim
Aureole, Halo around the Moon
Boy/Male
Arabic, Indian, Lebanese, Sanskrit, Swahili
Halo Around the Moon; Plough; Great; Dazzling; Sweetness
Male
German
Pet form of German Adolf, AHLF means "noble wolf."
Female
Welsh
Welsh name HAF means "summer."
Girl/Female
African, Arabic, Hindu, Indian, Lebanese, Muslim, Pashtun, Sanskrit, Swahili
Halo Around the Moon; Plough; Girlfriend; Great; Dazzling; Glorious; Lunar Halo; Glory; Golden; Female Friend; Sweetness; Outline of Brightness Surrounding a Full Moon
Male
German
Low German pet form of German Adolf, ALF means "noble wolf." Compare with other forms of Alf.
Male
Scandinavian
 Scandinavian form of Old Norse Ráðúlfr, RALF means "wise wolf." Compare with another form of Ralf.
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
Girl/Female
Tamil
Shravasti | à®·à¯à®°à®¾à®µà®¸à¯à®¤à¯€
An ancient indian city
Boy/Male
Tamil
Somjit | ஸோமà¯à®œà¯€à®¤
One who conquer the Sun
Boy/Male
American, Australian, British, Christian, English, French, Jamaican
Pomegranate Seed; Armed with a Spear; Spear; Red Like a Pomegranate; Dark Red Gem; Garnet (the Gem); Precious Stone
Boy/Male
Hindu
Great
Boy/Male
Indian
Wonderful
Boy/Male
Indian, Sanskrit
Young at Heart / Lord Shiva's Name
Boy/Male
Tamil
Heart bits
Boy/Male
Tamil
New
Surname or Lastname
English and Welsh
English and Welsh : variant of Purcell.
Girl/Female
Hindu, Indian
Born from Lotus; Lakshmi
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
HALF TRANSITIVE-GRAPH
n.
Half the length of a sword; close fight.
a.
Half-blooded.
a.
Imperfectly hatched; as, half-hatched eggs.
a.
Not transitive; not passing over to an object; expressing an action or state that is limited to the agent or subject, or, in other words, an action which does not require an object to complete the sense; as, an intransitive verb, e. g., the bird flies; the dog runs.
a.
Half-blooded.
a.
One of two equal parts into which anything may be divided, or considered as divided; -- sometimes followed by of; as, a half of an apple.
a.
Done or happening at intervals of half an hour.
adv.
In an equal part or degree; in some pa/ appro/mating a half; partially; imperfectly; as, half-colored, half done, half-hearted, half persuaded, half conscious.
a.
Consisting of a moiety, or half; as, a half bushel; a half hour; a half dollar; a half view.
a.
tropical; figurative; as, a translative sense.
n.
The shape of a half-moon; a crescent.
a.
Half-bred; imperfect.
a.
Consisting of some indefinite portion resembling a half; approximately a half, whether more or less; partial; imperfect; as, a half dream; half knowledge.
a.
Passing over to an object; expressing an action which is not limited to the agent or subject, but which requires an object to complete the sense; as, a transitive verb, for example, he holds the book.
a.
Half-filled.
n.
Passage from one place or state to another; charge; as, the transition of the weather from hot to cold.
a.
Half-demented; half-witted.
n.
See Half deck, under Deck.