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Complete bipartite cut in a graph
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits
Split_(graph_theory)
Graph which partitions into a clique and independent set
graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs
Split_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)
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
Adjacent subset of an undirected graph
In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are
Clique_(graph_theory)
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
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
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
Topics referred to by the same term
destroyer Split, decommissioned in 1980 Yugoslav frigate Split, Koni-class Split (graph theory) Split (mathematics), a property of an exact sequence Split Lie
Split
Graph where all long cycles have a chord
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not
Chordal_graph
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
Perfect graphs have neither odd holes nor odd antiholes
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither
Strong_perfect_graph_theorem
Graph with same nodes as but complementary connections to another
In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices are
Complement_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 with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
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
Method of graph decomposition
In graph theory, a haven is a certain type of function on sets of vertices in an undirected graph. If a haven exists, it can be used by an evader to win
Haven_(graph_theory)
Intersection graph for intervals on the real number line
In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge
Interval_graph
One of two types of graph
In graph theory, a book graph (often written B p {\displaystyle B_{p}} ) may be any of several kinds of graph formed by multiple cycles sharing an edge
Book_(graph_theory)
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Number of vertices with unambiguous distances
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as
Sphericity_(graph_theory)
Unsolved problem in computational complexity theory
bipartite Eulerian graphs bipartite regular graphs line graphs split graphs chordal graphs regular self-complementary graphs polytopal graphs of general, simple
Graph_isomorphism_problem
Measure of whether or not a graph has a "bottleneck"
Laplacian matrix of the graph. The Cheeger inequality is a fundamental result and motivation for spectral graph theory. Spectral graph theory Algebraic connectivity
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
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
Graph formed by adding isolated or universal vertices
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Threshold_graph
Topics referred to by the same term
matching theory - an economic theory studying desirable normative properties of matchings and developing rules that attain such matchings. Matching (graph theory)
Matching_theory
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate
Word-representable_graph
Fewest cliques covering a graph's edges
In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements
Intersection number (graph theory)
Intersection_number_(graph_theory)
Constructs with triply-connected vertices
2-connected graphs are defined as usual. This leaves the other graphs in the 3-connected class because each 3-regular graph can be split by cutting all
Table_of_simple_cubic_graphs
Flow graph invented by Claude Shannon
signal-flow graph theory builds on that of directed graphs (also called digraphs), which includes as well that of oriented graphs. This mathematical theory of
Signal-flow_graph
Characterization of graphs with perfect matchings
mathematical discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings
Tutte's theorem on perfect matchings
Tutte's_theorem_on_perfect_matchings
self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex-connected graph and a 1-edge-connected graph. A graph is bull-free
Bull_graph
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Graovac (15 July 1945 in Split – 13 November 2012 in Zagreb) was a Croatian scientist known for his contribution to chemical graph theory. He was director of
Ante_Graovac
Subset of a graph's nodes such that all other nodes link to at least one
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination
Dominating_set
In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t-tough for a given real number t if, for every integer
Graph_toughness
Academic journal
applications of combinatorics. Series B is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and
Journal of Combinatorial Theory
Journal_of_Combinatorial_Theory
Problem of finding the longest simple path for a given graph
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A
Longest_path_problem
Distance of a graph from a split graph
In graph theory, a branch of mathematics, the splittance of an undirected graph measures its distance from a split graph. A split graph is a graph whose
Splittance
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Intersection graph of trapezoids between parallel lines
In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that
Trapezoid_graph
Theorem in graph theory
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number
Menger's_theorem
Graph whose induced subgraphs preserve distance
In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances
Distance-hereditary_graph
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
automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a
Noncommutative signal-flow graph
Noncommutative_signal-flow_graph
In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels
Radio_coloring
Family of graphs whose shallow minors are sparse graphs
In graph theory, a family of graphs is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse
Bounded_expansion
Partition of the vertices of a graph
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure
Gallai–Edmonds_decomposition
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 formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
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
Cycles in a graph that cover each edge twice
every bridgeless graph have a multiset of cycles covering every edge exactly twice? More unsolved problems in mathematics In graph-theoretic mathematics
Cycle_double_cover
In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs G and H is a graph that is an induced subgraph of both
Maximum common induced subgraph
Maximum_common_induced_subgraph
Generalised concept of incidence structure of polygons
Combinatorial Theory, Series B. 100 (5): 439–445. doi:10.1016/j.jctb.2010.01.003. Godsil, Chris; Royle, Gordon (2001), Algebraic Graph Theory, Graduate Texts
Generalized_polygon
Problem of finding a cycle through all vertices of a graph
theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly
Hamiltonian_path_problem
Representation of a graph's triconnected components
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex
SPQR_tree
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
In graph theory and computer science, the graph sandwich problem is a problem of finding a graph that belongs to a particular family of graphs and is
Graph_sandwich_problem
Dominating set that dominates both a graph and its complement
In graph theory, a global dominating set is a dominating set S {\displaystyle S} of a graph G {\displaystyle G} that is also a dominating set of the complement
Global_dominating_set
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
Mathematical concept
the topological one, as applied to graphs, but it is easier to deal with in the context of graph theory. Graph theory also offers a context-free measure
Connectedness
Academic journal
signal processing, systems and control theory, statistics, Markov chains, mathematical biology, graph theory, and data science. The journal was originally
SIAM Journal on Matrix Analysis and Applications
SIAM_Journal_on_Matrix_Analysis_and_Applications
Form taken by the network of interconnections of a circuit
of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can
Circuit_topology_(electrical)
In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has
Chordal_bipartite_graph
Technique for drawing non-planar graphs
mathematical field of graph theory, planarization is a method of extending graph drawing methods from planar graphs to graphs that are not planar, by
Planarization
Hungarian-American mathematician and computer scientist
on 2016-01-21. Theory of Computing editors, retrieved 2010-07-30. A Big Result On Graph Isomorphism // November 4, 2015, A Fast Graph Isomorphism Algorithm
László_Babai
Graphs whose distances obey Ptolemy's inequality
In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek
Ptolemaic_graph
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Recursively splitting a graph into subsets of nodes
In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected
Modular_decomposition
Belarusian mathematician (1929–2019)
1929 – 17 November 2019) was a Belarusian mathematician, an expert in graph theory, Doctor of Physical and Mathematical Sciences, professor of the Belarusian
Regina_Tyshkevich
Process of generalization
they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see
Abstraction
Social structure made up of a set of social actors
social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads
Social_network
Graph where any two induced paths between nodes both have odd or even lengths
In graph theory, a parity graph is a graph in which all induced paths between the same two vertices have the same parity: either all paths have odd length
Parity_graph
Study of Lie groups, Lie algebras and differential equations
instance of Lie theory. The compact case arises through Euler's formula in the complex plane. Other one-parameter groups occur in the split-complex number
Lie_theory
Mathematical method in graph theory
after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for
Euler_tour_technique
Path-finding using high-weight graph edges
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight
Widest_path_problem
Graph coloring with equal color classes
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No
Equitable_coloring
Clustering and community detection algorithm
function aggregateGraph returns a new graph whose vertices are the partition of the old graph, and whose edges are calculated using the old graph. This function
Louvain_method
Mathematical models of strategic interactions
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively
Game_theory
Clustering and community detection algorithm
split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each
Leiden_algorithm
Models signal dispersion by representing the radio propagation environment by a graph
Propagation graphs are a mathematical modelling method for radio propagation channels. A propagation graph is a signal flow graph in which vertices represent
Propagation_graph
Pictorial representation of symmetry
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a
Dynkin_diagram
specializing in potential theory Jo Ellis-Monaghan, American mathematician interested in graph polynomials and topological graph theory Maria Emelianenko, Russian-American
List_of_women_in_mathematics
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 into
Planar_separator_theorem
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
Measure of graph complexity
In graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth
Clique-width
Colorings of Hypergraphs. 4th Southeastern Conference on Combinatorics, Graph Theory, and Computing. Håstad, Johan (2001). "Some Optimal Inapproximability
Set_splitting_problem
Index of articles associated with the same name
"past → future" form. Planar separator theorem (graph theory) states that any planar graph can be split into smaller pieces by removing a small number
Separation_theorem
Ancient proverb
Harary described how balance theory can predict coalition formation in international relations: One can draw the signed graph of a given state of events
The enemy of my enemy is my friend
The_enemy_of_my_enemy_is_my_friend
Mathematical measure for partial orders
(planar graph with fixed plane embedding) is at most four. Felsner later proved in "The order dimension of planar maps revisited " that dim ( split ( P M
Order_dimension
Highly connected subgraph
In graph theory and computer science, a dense subgraph is a subgraph with many edges per vertex. This is formalized as follows: let G = (V, E) be an undirected
Dense_subgraph
In the mathematical field of graph theory, the Tutte 12-cage or Benson graph is a 3-regular graph with 126 vertices and 189 edges. It is named after W
Tutte_12-cage
Graphical technique for data sets
plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be
Plot_(graphics)
Analog of the continuous Laplace operator
operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices)
Discrete_Laplace_operator
Partition refinement forms a key component of several efficient algorithms on graphs and finite automata, including DFA minimization, the Coffman–Graham algorithm
Partition_refinement
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link
Alternating_knot
Theory of categorization in psychology
Prototype theory is a theory of categorization in cognitive science, particularly in psychology and cognitive linguistics, in which there is a graded degree
Prototype_theory
permutation is skew-merged if and only if its associated permutation graph is a split graph, a graph that can be partitioned into a clique (corresponding to the
Skew-merged_permutation
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
Boy/Male
Muslim
Strong, Solid, Firm, Sharp
Boy/Male
Arabic, Muslim, Sindhi
Split
Girl/Female
Muslim
Grape vine
Boy/Male
American, British, English
From the Split Meadow
Boy/Male
Arabic, Modern
Grape
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Muslim
Grape like
Boy/Male
Tamil
Inside viewer, Spilt second
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Muslim
Grape
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
American, Christian, Hebrew, Indian
Narrow Split of Land
Boy/Male
Muslim/Islamic
Split Cleavage
Girl/Female
Indian
Grape like
Boy/Male
English
From the split meadow.
Boy/Male
Muslim
Split, Cleavage
Boy/Male
Indian
Grape
Boy/Male
Arabic, Muslim
Strong; Solid; Firm; Sharp
Girl/Female
Hindu, Indian
Momentary; Split Second
Girl/Female
Indian
Grape vine
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
Boy/Male
Tamil
Satyadarshi | ஸதà¯à®¯à®¾à®¤à®°à¯à®·à¯€
One who can see the truth
Girl/Female
Muslim
Heart-ravishing
Girl/Female
Indian
Circumstances
Girl/Female
Latin
Hard working.
Boy/Male
Tamil
Girl/Female
Indian, Modern, Telugu
Princess / Queen
Boy/Male
American, British, English
From the Bank
Girl/Female
Indian
Guardian, Protector
Boy/Male
Hindu
Work, Achievement, Worship
Boy/Male
Celtic American Gaelic Scottish
Crooked nose. Nickname of a Highland chieftain with a crooked nose.
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
SPLIT GRAPH-THEORY
imp. & p. p.
of Slit
v. t.
To divide or separate into components; -- often used with up; as, to split up sugar into alcohol and carbonic acid.
n.
the substitution of more than one share of a corporation's stock for one share. The market price of the stock usually drops in proportion to the increase in outstanding shares of stock. The split may be in any ratio, as a two-for-one split; a three-for-two split.
n.
To cut lengthwise; to cut into long pieces or strips; as, to slit iron bars into nail rods; to slit leather into straps.
v. t.
To divide lengthwise; to separate from end to end, esp. by force; to divide in the direction of the grain layers; to rive; to cleave; as, to split a piece of timber or a board; to split a gem; to split a sheepskin.
v. t.
Splint, or splent, coal. See Splent coal, under Splent.
v. t.
To split into splints, or thin, slender pieces; to splinter; to shiver.
v. t.
One of the small plates of metal used in making splint armor. See Splint armor, below.
imp. & p. p.
of Split
n.
A piece that is split off, or made thin, by splitting; a splinter; a fragment.
v. i.
To part asunder; to be rent; to burst; as, vessels split by the freezing of water in them.
imp. & p. p.
of Spit
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
v. t.
To fasten or confine with splints, as a broken limb. See Splint, n., 2.
a.
Divided; split; partly divided or split.
v. t.
A piece split off; a splinter.
v. i.
To attend to a spit; to use a spit.
v. t.
A disease affecting the splint bones, as a callosity or hard excrescence.
v. t.
A splint bone.