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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 with tight clique-coloring relation
associated graphs. The perfect graph theorem states that the complement graph of a perfect graph is also perfect. The strong perfect graph theorem characterizes
Perfect_graph
Unrelated vertices in graphs
edge in the graph has at most one endpoint in S {\displaystyle S} . A set is independent if and only if it is a clique in the graph's complement. The size
Independent set (graph theory)
Independent_set_(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 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
16-regular graph with 27 vertices and 216 edges
graph with parameters srg(27, 16, 10, 8). The intersection graph of the 27 lines on a cubic surface is a locally linear graph that is the complement of
Schläfli_graph
Concept in graph theory
μ common neighbours. Such a strongly regular graph is denoted by srg(v, k, λ, μ). Its complement graph is also strongly regular: it is an srg(v, v −
Strongly_regular_graph
Vertices connected in pairs by edges
as: edge contraction, line graph, dual graph, complement graph, graph rewriting; binary operations, which create a new graph from two initial ones, such
Graph_(discrete_mathematics)
Graph in which every two vertices are adjacent
disconnects the graph is the complete set of vertices. The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each
Complete_graph
Topics referred to by the same term
complement Two's complement Complement graph Self-complementary graph, a graph which is isomorphic to its complement Complemented lattice Complement of an angle
Complement
Order-zero graph or any edgeless graph
mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes
Null_graph
Complements of perfect graphs are perfect
In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph
Perfect_graph_theorem
Type of knowledge base
this knowledge graph have been further organized using terms from the schema.org vocabulary. The Google Knowledge Graph became a complement to string-based
Knowledge_graph
Adjacent subset of an undirected graph
graph or its complement graph contains a clique with at least a logarithmic number of vertices. According to a result of Moon & Moser (1965), a graph
Clique_(graph_theory)
Graph able to be partitioned into multiple independent sets
one vertex. Complete k-partite graphs, complete multipartite graphs, and their complement graphs, the cluster graphs, are special cases of cographs,
Multipartite_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
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Graph divided into two independent sets
graphs: every bipartite graph, the complement of every bipartite graph, the line graph of every bipartite graph, and the complement of the line graph
Bipartite_graph
Graph made from disjoint union of complete graphs
graph if and only if it has no three-vertex induced path; for this reason, the cluster graphs are also called P3-free graphs. They are the complement
Cluster_graph
On bipartite matching and vertex cover
graphs are perfect, the complements of line graphs of bipartite graphs are also perfect. A clique in the complement of the line graph of G is just a matching
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Task of computing complete subgraphs
have been developed for many subclasses of perfect graphs. In the complement graphs of bipartite graphs, Kőnig's theorem allows the maximum clique problem
Clique_problem
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
Procedures for constructing new graphs in graph theory
graph from an initial one by a complex change, such as: transpose graph; complement graph; line graph; graph minor; graph rewriting; power of graph;
Graph_operations
Subgraph induced by all nodes linked to a given node of a graph
that is, for all vertices, the complement graph of the neighbourhood of the vertex does not contain a triangle. A graph that is locally H is claw-free
Neighbourhood_(graph_theory)
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Abstract simplicial complex describing a graph's cliques
complex of the complement graph of the line graph of the given graph. When the matching complex is referred to without any particular graph as context, it
Clique_complex
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
of time. Every interval graph is a tolerance graph. The complement graph of every tolerance graph is a perfectly orderable graph, from which it follows
Tolerance_graph
countably infinite), their complement graphs, the Henson graphs together with their complement graphs, and the Rado graph. If a graph is 5-ultrahomogeneous
Homogeneous_graph
Binary operation combining the vertex and edge sets of two graphs
In graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is
Disjoint_union_of_graphs
Upper bound on a graph's Shannon capacity
complement of any graph is sandwiched between the chromatic number and clique number of the graph, and can be used to compute these numbers on graphs
Lovász_number
graph is a clique in its complement graph, and vice versa. Therefore, the independence complex of a graph equals the clique complex of its complement
Independence_complex
Perfect graphs have neither odd holes nor odd antiholes
bipartite graphs, line graphs of bipartite graphs, complementary graphs of bipartite graphs, complements of line graphs of bipartite graphs, and double
Strong_perfect_graph_theorem
Cubic graph with 10 vertices and 15 edges
rational tropical curves. The Petersen graph is the complement of the line graph of K5. It is also the Kneser graph KG5,2; this means that it has one vertex
Petersen_graph
Graph which is isomorphic to its complement
of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are
Self-complementary_graph
Bipartite, 3-regular undirected graph
nine-vertex graph is 6-regular, is the complement graph of the union of three disjoint triangle graphs, and is the complete tripartite graph K3,3,3. The
Pappus_graph
Graph where all pairs of vertices are automorphic
vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertices is vertex-transitive
Vertex-transitive_graph
Graph without four-vertex star subgraphs
Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph. Claw-free graphs were initially studied
Claw-free_graph
Trail in which only the first and last vertices are equal
is the complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect
Cycle_(graph_theory)
One of two types of graph
{\displaystyle r} -vertex graph, either the graph itself contains B p {\displaystyle B_{p}} as a subgraph, or its complement graph contains B q {\displaystyle
Book_(graph_theory)
Graph representing connectivity between cliques of another graph
length four or more is a gear graph. The simplex graph of the complement graph of a path graph is a Fibonacci cube. The complete subgraphs of G can be given
Simplex_graph
Embedding of the circle in three dimensional Euclidean space
mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional
Knot_(mathematics)
Graph linking pairs of comparable elements in a partial order
graphs are a subclass of string graphs; the complement of every comparability graph is a string graph. Every complete graph is a comparability graph,
Comparability_graph
Family of graphs based on the Fibonacci sequence
graph of the complement graph of an n-vertex path graph. That is, each vertex in the Fibonacci cube represents a clique in the path complement graph,
Fibonacci_cube
Family of graphs with 2n nodes and n(n-1) edges
complete graph, as the tensor product Kn × K2, as the complement of the Cartesian direct product of Kn and K2, or as a bipartite Kneser graph Hn,1 representing
Crown_graph
Graph which partitions into a clique and independent set
involves complementation: they are chordal graphs the complements of which are also chordal. Just as chordal graphs are the intersection graphs of subtrees
Split_graph
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
Intersection graph for intervals on the real number line
complement is a comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph
Interval_graph
Partition of a graph's nodes into cliques
cover number of the given graph. A clique cover of a graph G may be seen as a graph coloring of the complement graph of G, the graph on the same vertex set
Clique_cover
a graph is integral, then so is its complement graph; for instance, the complements of complete graphs, edgeless graphs, are integral. If two graphs are
Integral_graph
Balanced complete multipartite graph
overall graph is the complement of the disjoint union of the complements of these independent sets. Chao & Novacky (1982) show that the Turán graphs are chromatically
Turán_graph
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
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
Graph path which is an induced subgraph
antihole is a hole in the complement of G, i.e., an antihole is a complement of a hole. The length of the longest induced path in a graph has sometimes been
Induced_path
Graph of numbers differing by a square
4 and queue number 3. The Paley graph of order 17 is the unique largest graph G such that neither G nor its complement contains a complete 4-vertex subgraph
Paley_graph
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Intersection graph for curves in the plane
graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if
String_graph
Dominating set that dominates both a graph and its complement
of a graph G {\displaystyle G} that is also a dominating set of the complement graph G ¯ {\displaystyle {\bar {G}}} . The global domination number γ g (
Global_dominating_set
Graph representing a permutation
permutation graph is polynomial in the size of the graph. Permutation graphs are a special case of circle graphs, comparability graphs, the complements of comparability
Permutation_graph
connected components (faces) of the complement of the graph. That is, it is a tessellation of the surface. A map graph is a graph derived from a map by creating
Map_(graph_theory)
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
Graph whose vertices correspond to combinations of a set of n elements
Kneser graph K(n, 2) is the complement of the line graph of the complete graph on n vertices. The Kneser graph K(2n − 1, n − 1) is the odd graph On; in
Kneser_graph
Edge-joined polygons which fold into a polyhedron
glued together to form a net, together with a perfect matching on the complement graph of the tree describing the pairs of faces that are opposite each other
Net_(polyhedron)
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
Characterizes the height of any finite partially ordered set
every complement graph of a comparability graph is perfect. The perfect graph theorem of Lovász (1972) states that the complements of perfect graphs are
Mirsky's_theorem
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)
Recursively splitting a graph into subsets of nodes
modules. A graph is prime if all its modules are trivial. Connected components of a graph G {\displaystyle G} , or of its complement graph are also modules
Modular_decomposition
Operation in graph theory
In graph theory, local complementation (also known as vertex inversion) is an operation on a graph that toggles adjacencies among the neighbours of a
Local_complementation
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
Distance-transitive cubic graph with 20 nodes and 30 edges
databases. The name "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
Desargues_graph
Mathematical object
faces are all independent sets of G (it is the clique complex of the complement graph of G). Clique complexes are the prototypical example of flag complexes
Abstract_simplicial_complex
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph) is a graph with an odd number of vertices in which deleting
Factor-critical_graph
Graph where every connected induced subgraph has a universal vertex
the graph is trivially perfect. The algorithm can also be modified to test whether a graph is the complement graph of a trivially perfect graph, in linear
Trivially_perfect_graph
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
Undirected unit-distance graph requiring four colors
convex vertices. The complement graph of the Moser graph is a triangle-free graph. Thus, the unit distance embedding of the Moser graph may be used to solve
Moser_spindle
Linear algebra aspects of graph theory
to 1. A pair of regular graphs are cospectral if and only if their complements are cospectral. A pair of distance-regular graphs are cospectral if and only
Spectral_graph_theory
Graph which can be made planar by removing a single node
In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called
Apex_graph
Graph whose induced subgraphs preserve distance
graph characterization according to which no induced subgraph can be a house (the complement graph of a five-vertex path graph), hole (a cycle graph of
Distance-hereditary_graph
One-by-one assignment of colors to graph vertices
} -perfect graphs. If a graph and its complement graph are both even-hole-free, they are both β {\displaystyle \beta } -perfect. The graphs that are both
Greedy_coloring
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
graphs, split graphs, or the complements of bipartite graphs. However it is solvable in polynomial time for trees and cographs. For arbitrary graphs,
Radio_coloring
Generalization of line graphs to hypergraphs
In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L(H), is the graph whose vertex set is the set of
Line_graph_of_a_hypergraph
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
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
Mathematical set formed from two given sets
complement }&A_{2}^{\complement }&\dots &A_{n}^{\complement }\\B_{1}^{\complement }&B_{2}^{\complement }&\dots &B_{n}^{\complement }\end{array}}\right[}
Cartesian_product
Branch of the mathematical field of graph theory
topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological
Topological_graph_theory
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
Class of undirected graphs defined from systems of sets
complete graph Kn. J ( 4 , 2 ) {\displaystyle J(4,2)} is the octahedral graph. J ( 5 , 2 ) {\displaystyle J(5,2)} is the complement of the Petersen graph, hence
Johnson_graph
Undirected graph with no non-trivial symmetries
asymmetric cubic graphs. The class of asymmetric graphs is closed under complements: a graph G is asymmetric if and only if its complement is. Any n-vertex
Asymmetric_graph
Maximum number of disjoint dominating sets
vertex, and (2) any graph has a weak 2-coloring. Alternatively, (1) a maximal independent set is a dominating set, and (2) the complement of a maximal independent
Domatic_number
Partition of a graph's nodes into 2 disjoint subsets
vector addition operation, and is the orthogonal complement of the cycle space. If the edges of the graph are given positive weights, the minimum weight
Cut_(graph_theory)
Independent set in a graph
In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E)
Rainbow-independent_set
Binary operation on graphs
graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H
Graph_product
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
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
Measure of graph complexity
of certain graphs: If a graph has clique-width at most k, then so does every induced subgraph of the graph. The complement graph of a graph of clique-width
Clique-width
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
Graph property
n-vertex graph is a linear forest, then μ ≥ n − 3; If the complement of an n-vertex graph is outerplanar, then μ ≥ n − 4; If the complement of an n-vertex
Colin de Verdière graph invariant
Colin_de_Verdière_graph_invariant
Special case of a strongly regular graph
{v}}}{2}},} each with multiplicity (v − 1)/2. The complement of a conference graph is always a conference graph with the same parameters, and in many cases
Conference_graph
Concept in extremal graph theory
its complement G ¯ {\displaystyle {\overline {G}}} must contain lots of copies of F {\displaystyle F} in order to compensate for it. Common graphs are
Common_graph
COMPLEMENT GRAPH
COMPLEMENT GRAPH
Boy/Male
Hindu
Competent, Powerful
Boy/Male
Anglo Saxon
Competent.
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Muslim/Islamic
Compliments happiness
Girl/Female
Indian
Competent
Boy/Male
Indian
Compliments, Happiness
Boy/Male
Japanese
Complacent; satisfied.
Boy/Male
Hindi
Competent.
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Muslim
Compliments, Happiness
Boy/Male
Muslim
Competent. Well disposed.
Boy/Male
Indian, Sanskrit
Competent
Boy/Male
Tamil
Sakshain | ஸாகà¯à®·à¯€à®¨
Competent, Powerful
Sakshain | ஸாகà¯à®·à¯€à®¨
Girl/Female
Indian
Competent.
Boy/Male
Muslim
Competent. Well disposed.
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Muslim
Competent
Girl/Female
Tamil
Fit, Competent, Administrator
Girl/Female
Hindu
Fit, Competent, Administrator
COMPLEMENT GRAPH
COMPLEMENT GRAPH
Female
English
Elaborated form of English Ruby, RUBINA means "ruby."
Boy/Male
Slavic Russian
Glory.
Boy/Male
Arabic, Indian, Muslim
Tamer
Boy/Male
Muslim
Prince
Female
German
Pet form of German Katarine, KATRIN means "pure."
Boy/Male
Muslim/Islamic
Of noble birth
Boy/Male
Muslim
The Biblical Jonas is the English language equivalent. A Prophet's name.
Girl/Female
Norse
New.
Girl/Female
Hindu, Indian
Dancing
Boy/Male
Australian, Scottish
Son of Fire
COMPLEMENT GRAPH
COMPLEMENT GRAPH
COMPLEMENT GRAPH
COMPLEMENT GRAPH
COMPLEMENT GRAPH
v. t.
That which is required to supply a deficiency, or to complete a symmetrical whole.
v. t.
To supply a lack; to supplement.
n.
Compilation.
v. t.
Full quantity, number, or amount; a complete set; completeness.
v. t.
A compliment.
v. t.
To compliment.
v. t.
A second quantity added to a given quantity to make it equal to a third given quantity.
v. t.
The interval wanting to complete the octave; -- the fourth is the complement of the fifth, the sixth of the third.
n.
Compliments; greetings.
v. t.
The whole working force of a vessel.
n.
Union; combination; a coupling; a pair.
v. t.
To praise, flatter, or gratify, by expressions of approbation, respect, or congratulation; to make or pay a compliment to.
v. i.
To pass compliments; to use conventional expressions of respect.
a.
Self-satisfied; contented; kindly; as, a complacent temper; a complacent smile.
n.
An expression, by word or act, of approbation, regard, confidence, civility, or admiration; a flattering speech or attention; a ceremonious greeting; as, to send one's compliments to a friend.
v. t.
Something added for ornamentation; an accessory.
n.
The nest complement of eggs of a bird.
v. t.
To provide with an implement or implements; to cause to be fulfilled, satisfied, or carried out, by means of an implement or implements.
n. pl.
Respects; compliments.
v. t.
That which fills up or completes; the quantity or number required to fill a thing or make it complete.