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Type of graph in mathematics
In graph theory, a branch of mathematics, a half graph is a special type of bipartite graph. These graphs are called the half graphs because they have
Half_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
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
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
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
Graph of short distances in another graph
In graph theory, a branch of mathematics, the kth power Gk of an undirected graph G is another graph that has the same set of vertices, but in which two
Graph_power
Distance-transitive cubic graph with 20 nodes and 30 edges
"Desargues graph" has also been used to refer to a ten-vertex graph, the complement of the Petersen graph, which can also be formed as the bipartite half of the
Desargues_graph
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
Graph that misrepresents data
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the
Misleading_graph
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
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
Graph whose edges are given independent directions at both ends
neither half nor loose edges may be called ordinary edges. A skew-symmetric graph is the double covering graph of a bidirected graph. A bidirected graph may
Bidirected_graph
Graph whose nodes are one of the vertex sets of a bipartite graph
In graph theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition
Bipartite_half
Embedding a graph in a topological space, often Euclidean
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation
Graph_embedding
Graph data structure
edge list (DCEL), also known as half-edge data structure, is a data structure to represent an embedding of a planar graph in the plane, and polytopes in
Doubly_connected_edge_list
Polynomial function of degree 3
monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around
Cubic_function
Intersection graph representing regions on the Euclidean plane
In graph theory, a branch of mathematics, a map graph is an undirected graph formed as the intersection graph of finitely many simply connected and internally
Map_graph
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
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
Graph of the vertices and edges of a demihypercube
In graph theory, the halved cube graph or half cube graph of dimension n is the vertex-edge graph of the demihypercube, formed by connecting pairs of vertices
Halved_cube_graph
Class of undirected graphs defined from systems of sets
mathematics, Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J ( n , k ) {\displaystyle
Johnson_graph
in the first half of the path form the same sequence as the colors of the edges in the second half of the path. The Thue number of a graph is the minimum
Thue_number
Graph with a list of distinguished cycles
satisfies the theta-graph property mentioned above.) A subgraph or edge set whose circles are all in B (and which contains no half-edges) is called balanced
Biased_graph
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Graph partition into regular subgraphs
In extremal graph theory, Szemerédi's regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between
Szemerédi_regularity_lemma
Two special graphs in graph theory
transitively on its half-edges, so the Klein graph is a symmetric graph. The characteristic polynomial of this 56-vertex Klein graph is equal to x 7 ( x
Klein_graphs
in mathematics In graph theory, an overfull graph is a graph whose size is greater than the product of its maximum degree and half of its order floored
Overfull_graph
Partition of a graph's nodes into 2 disjoint subsets
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one
Cut_(graph_theory)
Second-smallest eigenvalue of a graph Laplacian
known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately)
Algebraic_connectivity
mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible
Minimum bottleneck spanning tree
Minimum_bottleneck_spanning_tree
Cubic graph with 8 vertices and 12 edges
mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder
Wagner_graph
Graph which is isomorphic to its complement
The Rado graph is an infinite self-complementary graph. An n-vertex self-complementary graph has exactly half as many edges of the complete graph, i.e.,
Self-complementary_graph
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Multi-lobed plane curve
sinusoids that specify them. Graphs of roses are composed of petals. A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies
Rose_(mathematics)
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
Chart indicator of moving average convergence/divergence
number 2 above is often preferred. Histogram: Gerald Appel referred to bar graph plots of the basic MACD time series as "histogram". In Appel's Histogram
MACD
Periodic spatial graph
Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three
Laves_graph
Maximum number of colors obtainable by a greedy graph coloring algorithm
In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring
Grundy_number
Graph database implemented in Java
global graph intelligence company that provides technology for analyzing and managing connected data. It is most known for creating the Neo4j Graph database
Neo4j
Type of geometric spanner graph
computational geometry, the Theta graph, or Θ {\displaystyle \Theta } -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction
Theta_graph
Least-weight tree connecting graph vertices
tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the
Minimum_spanning_tree
Trees with additional directed half edges
planar graphs, blossom trees are trees with additional directed half edges. Each blossom tree is associated with an embedding of a planar graph. Blossom
Blossom_tree_(graph_theory)
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
Measure of whether or not a graph has a "bottleneck"
(also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Graphical representation of energy flows in physical systems
A bond graph is a graphical representation of the energy flows though and between physical dynamical systems including those in the electrical, mechanical
Bond_graph
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
24-vertex symmetric bipartite cubic graph
In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David
Nauru_graph
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
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
Graph without four-vertex star subgraphs
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the
Claw-free_graph
Abstract regular polyhedron with 10 triangular faces
5-simplex which has a complete graph of edges, but only contains half of the (20) faces. From the point of view of graph theory this is an embedding of
Hemi-icosahedron
Bipartite 3-regular graph with 90 vertices and 135 edges
cubic symmetric graphs included this graph. The bipartite half of the Foster graph is a distance-regular graph and a locally linear graph. It is one of
Foster_graph
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
Decrease in value at a rate proportional to the current value
"half-life". A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of
Exponential_decay
Graph with sign-labeled edges
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if
Signed_graph
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
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
On tangency patterns of circles
whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph having a vertex for each circle, and an edge
Circle_packing_theorem
Extremal graph theory bound on clique-free graph edges
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given
Turán's_theorem
Classic problem in graph theory
proof of impossibility by Leonhard Euler, in 1736, laid the foundations of graph theory and foreshadowed the idea of topology. The city of Königsberg in
Seven_Bridges_of_Königsberg
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
Graph rewriting framework
computer science, double pushout graph rewriting (or DPO graph rewriting) refers to a mathematical framework for graph rewriting. It was introduced as
Double pushout graph rewriting
Double_pushout_graph_rewriting
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
In graph theory, a fractional matching is a generalization of a matching in which, intuitively, each vertex may be broken into fractions that are matched
Fractional_matching
Book cataloguing social website
The StoryGraph (or simply StoryGraph) is a social book cataloging platform launched in 2019. Users can rate and review books, keep track of books they
The_StoryGraph
Type of graph in mathematics and physics
mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a
Quantum_graph
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
Proposition on the domination number of Cartesian products of graphs
mathematics In graph theory, Vizing's conjecture concerns a relation between the domination number and the cartesian product of graphs. This conjecture
Vizing's_conjecture
Graph theory problem: find a matching containing the most edges
In graph theory, a maximum-cardinality matching is a special kind of subgraph useful in many computational contexts. Given a graph G, a matching is a
Maximum-cardinality_matching
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
Data organization and storage formats
connected edge list also known as half-edge Difference list Free list Trees are a subset of directed acyclic graphs. AA tree AVL tree Binary search tree
List_of_data_structures
Line segment joining two adjacent vertices in a polygon or polytope
half-planes. The sides of a plane angle are semi-infinite half-lines (or rays). In graph theory, an edge is an abstract object connecting two graph vertices
Edge_(geometry)
2002 science fiction novel by Australian author Greg Egan
in "Quantum Graph Theory", which holds that physical existence can be precisely modelled by complex constructions of mathematical graphs. However, the
Schild's_Ladder
Concept in science
normalization in graph Laplacian and explainability of spectral clustering for signed graph partitioning; e.g., Similarly, in spectral graph theory, the eigenvalues
Negative_probability
1979 conjecture in combinatorics
most half of the graph's maximal independent sets. This conjecture is known to hold for chordal bipartite graphs, bipartite series–parallel graphs, and
Union-closed_sets_conjecture
Arctangent function with two arguments
Mathematica classifies ArcTan[0,0] as an indeterminate expression. On most TI graphing calculators (excluding the TI-85 and TI-86), the equivalent function is
Atan2
Open problem on 3x+1 and x/2 functions
13, 40, 20, 10, 5, 16, 8, 4, 2, 1 . The sequence for n = 27, listed and graphed below, takes 111 steps (41 steps through odd numbers, in bold), climbing
Collatz_conjecture
Mathematical puzzle of avoiding crossings
can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices
Three_utilities_problem
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
Problem in graph theory
In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary
Maximum_cut
Independent set which is not a subset of any other independent set
In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. In other
Maximal_independent_set
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
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Graph-theoretic description of polyhedra
planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are
Steinitz's_theorem
Conjecture in graph theory
In graph theory, Hedetniemi's conjecture, formulated by Stephen T. Hedetniemi in 1966, concerns the connection between graph coloring and the tensor product
Hedetniemi's_conjecture
1995 is now regarded as the driest. Only a few places registered more than half their average summer rainfall. In the Central England temperature record
1976_British_Isles_heatwave
Human mortality as a result of coronavirus disease 2019 (COVID-19)
WHO reports, tables, and spreadsheets. There are also maps and timeline graphs of daily and weekly deaths worldwide. 7,114,321 (updated 6 June 2026) confirmed
COVID-19_pandemic_deaths
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
Family of graphs based on the Fibonacci sequence
In the mathematical field of graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties
Fibonacci_cube
Graph showing the free energy vs oxidation state of a chemical species
A Frost diagram or Frost–Ebsworth diagram is a type of graph used by inorganic chemists in electrochemistry to illustrate the relative stability of a
Frost_diagram
of the graph Γ. First of all, to each graph there is a multiplicity m(Γ) which counts how many equivalent configurations there are for one graph. The rule
Kontsevich quantization formula
Kontsevich_quantization_formula
graph diameter of G, and A(n) is the n-graph neighborhood of A. Note that the maximization ranges over subsets A of G, subject to A being over half the
Lévy_family_of_graphs
On converting relations to functions of several real variables
provides the upper half of the circle. Similarly, if g 2 ( x ) = − 1 − x 2 {\displaystyle g_{2}(x)=-{\sqrt {1-x^{2}}}} , then the graph of y = g2(x) gives
Implicit_function_theorem
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
Graph with equal-size maximal independent sets
In graph theory, a well-covered graph is an undirected graph in which the minimal vertex covers all have the same size. Here, a vertex cover is a set
Well-covered_graph
Method for deriving motion equations using calculus
(see the acceleration zero crossings in the graphs below) depend on rod length l {\displaystyle l} and half stroke r {\displaystyle r} and do not occur
Piston_motion_equations
Polytope constructed from alternation of a hypercube
facets but are all uniform polytopes. The vertex-edge graph of the demihypercube is the halved cube graph. An n-demicube has inversion symmetry if n is even
Demihypercube
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
HALF GRAPH
HALF GRAPH
Male
English
Pet form of English Henry, HAL means "home-ruler."
Male
Scandinavian
Scandinavian form of Old Norse Alfr, ALF means "elf." Compare with other forms of Alf.
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
Latin
Half man half horse.
Male
German
Low German pet form of German Adolf, ALF means "noble wolf." Compare with other forms of Alf.
Boy/Male
English Swedish Teutonic
Lives in the hall.
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
Boy/Male
Christian & English(British/American/Australian)
From the Hall or Manor
Girl/Female
Indian
Aureole, Halo around the Moon
Boy/Male
American, Australian, British, English, German, Norse, Scandinavian, Teutonic
Half Dane; Half-danish
Female
Welsh
Welsh name HAF means "summer."
Boy/Male
Arabic, Indian, Lebanese, Sanskrit, Swahili
Halo Around the Moon; Plough; Great; Dazzling; Sweetness
Male
Scandinavian
 Scandinavian form of Old Norse Ráðúlfr, RALF means "wise wolf." Compare with another form of Ralf.
Male
English
Short form of English Alfred, ALF means "elf counsel." Compare with other forms of Alf.
Male
German
Pet form of German Adolf, AHLF means "noble wolf."
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
American, Anglo, Australian, British, Christian, English, French, German, Teutonic
Ingenious; From the Hall; Healthy Hero
Girl/Female
Muslim
Aureole, Halo around the Moon
Boy/Male
Norse
Half son of Asgeir.
Girl/Female
Muslim
Lunar halo. Glory.
HALF GRAPH
HALF GRAPH
Surname or Lastname
English (Devon)
English (Devon) : habitational name from Kennicott in Devon.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Sanskrit, Telugu
Renowned for his Devotion to his Guru
Girl/Female
Tamil
A kind of necklace, Auspicious symbol
Boy/Male
Arabic, Muslim
Pardon; Forgiveness
Boy/Male
Muslim
Thankful of anybody, Satisfied, Contended, Pleased
Female
Hebrew
(×ֱלִיש×ֶבַע) Hebrew name ELIYSHEBA means "God is my oath." In the Old Testament bible, this is the name of the wife of Aaron.Â
Girl/Female
American, Australian, British, English
A Fair Share
Girl/Female
Tamil
Jyeshtha | ஜà¯à®¯à¯‡à®·à¯à®Ÿ
Star name, Eldest daughter, A Nakshatra, The eldest, Lord Vishnu
Boy/Male
Tamil
Mrithun | à®®à¯à®°à¯€à®¤à¯à®¨Â
Boy/Male
Hindu, Indian, Sanskrit
Life
HALF GRAPH
HALF GRAPH
HALF GRAPH
HALF GRAPH
HALF GRAPH
a.
Half-blooded.
a.
Half-filled.
n.
Half the length of a sword; close fight.
n.
See Half deck, under Deck.
a.
Of half the whole or ordinary length, as a picture.
a.
Half-blooded.
a.
Half-demented; half-witted.
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.
n.
One half of a shutter made in two parts for closing a porthole.
n.
The moon at the quarters, when half its disk appears illuminated.
v. t. & i.
To form, or surround with, a halo; to encircle with, or as with, a halo.
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.
Half-bred; imperfect.
a.
Consisting of a moiety, or half; as, a half bushel; a half hour; a half dollar; a half view.
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.
n.
The shape of a half-moon; a crescent.
n.
A person whose father and mother are of different races; a half-breed.
a.
Imperfectly hatched; as, half-hatched eggs.
a.
Done or happening at intervals of half an hour.