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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
Type of chart
A line chart or line graph, also known as curve chart, is a type of chart that displays information as a series of data points called 'markers' connected
Line_chart
independence number of its line graph. Similarly, χ(G) is the chromatic number of a graph; χ ′(G) is the chromatic index of the graph, which equals the chromatic
Glossary_of_graph_theory
Graph of chess rook moves
mathematics of graphs through their alternative constructions: rook's graphs are the Cartesian product of two complete graphs, and are the line graphs of complete
Rook's_graph
Graph where every edge is in one triangle
Examples of locally linear graphs include the triangular cactus graphs, the line graphs of 3-regular triangle-free graphs, and the Cartesian products
Locally_linear_graph
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Graph whose line graph is perfect
In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple
Line_perfect_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
Bijection between the vertex set of two graphs
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to
Graph_isomorphism
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
On bipartite matching and vertex cover
the line graph of a bipartite graph is perfect. Since line graphs of bipartite graphs are perfect, the complements of line graphs of bipartite graphs are
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
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 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 that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Undirected graph named after S. S. Shrikhande
mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices
Shrikhande_graph
Methodic assignment of colors to elements of a graph
coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex
Graph_coloring
Planar graph embedding where edges map to straight-line segments
and geometric graph theory, a planar straight-line graph (PSLG), also called a straight-line plane graph or plane straight-line graph, is an embedding
Planar_straight-line_graph
Vertices connected in pairs by edges
related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for
Graph_(discrete_mathematics)
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
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
Study of graphs defined by geometric means
geometric and topological graphs" (Pach 2013). Geometric graphs are also known as spatial networks. A planar straight-line graph is a graph in which the vertices
Geometric_graph_theory
Canada holds general elections, colloquially referred to as federal elections since the 1940s (and as dominion elections from 1867 to the 1940s), for the
List of Canadian federal elections
List_of_Canadian_federal_elections
Path in a graph that visits each vertex exactly once
corresponds to a Hamiltonian cycle in the line graph L(G), so the line graph of every Eulerian graph is Hamiltonian. Line graphs may have other Hamiltonian cycles
Hamiltonian_path
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
A Digital Line Graph (DLG) is a cartographic map feature represented in digital vector form that is distributed by the U.S. Geological Survey (USGS). DLGs
Digital_line_graph
Basic concept of graph theory
mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that
Connectivity_(graph_theory)
Class of undirected graphs defined from systems of sets
hence the line graph of K5. More generally, for all n {\displaystyle n} , the Johnson graph J ( n , 2 ) {\displaystyle J(n,2)} is the line graph of Kn and
Johnson_graph
Graph representing intersections between given sets
In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an
Intersection_graph
(circular) or a cartesian coordinate (rectangular) graph, and either a line graph or a bar graph. In polar form, the months of the year are marked around
Ergograph
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 without four-vertex star subgraphs
mathematical research papers and several surveys. The line graph L ( G ) {\displaystyle L(G)} of any graph G {\displaystyle G} is claw-free. L ( G ) {\displaystyle
Claw-free_graph
File format
DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename
DOT (graph description language)
DOT_(graph_description_language)
Topics referred to by the same term
Look up Graph, graph, or -graph in Wiktionary, the free dictionary. Wikimedia Commons has media related to Graphs. Graph may refer to: Graph (discrete
Graph
In graph theory, the shift graph Gn,k for n , k ∈ N , n > 2 k > 0 {\displaystyle n,k\in \mathbb {N} ,\ n>2k>0} is the graph whose vertices correspond
Shift_graph
Graph whose biconnected components are all cliques
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component
Block_graph
Cumulative Frequency Graph
ogive is obtained by connecting each of the points to its neighbours with line segments. Sometimes an axis for both the absolute frequency and relative
Ogive_(statistics)
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
Graph with oriented edges
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed
Directed_graph
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)
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
Decomposition of a graph into hamiltonion cycles
In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles
Hamiltonian_decomposition
Type of chart
bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line. The chart
Pareto_chart
Type of incidence structure
other a line and the point lies on the line. The incidence graph of a generalized quadrangle is characterized by being a connected, bipartite graph with
Generalized_quadrangle
Adding edges to make a graph Hamiltonian
certain classes of graphs, including series–parallel graphs and their subgraphs, which include outerplanar graphs, as well as for a line graph of a tree or
Hamiltonian_completion
Number of vertices with unambiguous distances
bounded-degree planar graphs, split graphs, bipartite graphs and their complements, line graphs of bipartite graphs, unit disk graphs, interval graphs of diameter
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Directed graph representing overlaps between sequences of symbols
In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices
De_Bruijn_graph
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
Graph of king moves on a chessboard
In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square
King's_graph
Partition of a simple polygon into triangles
cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Over time, a number of algorithms
Polygon_triangulation
parameters and spectrum as the line graph L(K8) of the complete graph K8. Each of these three graphs may be obtained by graph switching from L(K8). That is
Chang_graphs
makes extensive use of graphs to better illustrate the economic principles and trends it is attempting to explain. Those graphs have specific qualities
Economic_graph
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
Line graph used in physical science
A cooling curve is a line graph that represents the change of phase of matter, typically from a gas to a solid or a liquid to a solid. The independent
Cooling_curve
Application of statistical techniques to biological systems
genes in ten operons of the same organism. Genes = {2,3,3,4,5,3,3,3,3,4} Line graphs represent the variation of a value over another metric, such as time
Biostatistics
The line graph of a regular integral graph is again integral. For instance, as the line graph of K 4 {\displaystyle K_{4}} , the octahedral graph is integral
Integral_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 all vertices of degree 4
mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph. Several well-known
Quartic_graph
measures of graph comprehension have tended to focus on the comprehension of specific features or types of graphs (e.g., line or bar graphs), incorporate
Graph_literacy
and the medial axis of M {\displaystyle M} . Given a planar straight-line graph, the local feature size at any point x {\displaystyle x} is the radius
Local_feature_size
Construct in computational geometry
Delaunay triangulation problem is a planar straight-line graph, a set of points and non-crossing line segments in the plane. The constrained Delaunay triangulation
Constrained Delaunay triangulation
Constrained_Delaunay_triangulation
Tree graph with all nodes within distance 1 from central path
represented as non-crossing line segments that have one endpoint on each line. They are the trees whose square is a Hamiltonian graph. That is, in a caterpillar
Caterpillar_tree
Graph representing a permutation
reversed by the permutation. Permutation graphs may also be defined geometrically, as the intersection graphs of line segments whose endpoints lie on two parallel
Permutation_graph
set in the square of the line graph of the given graph. The minimum number of induced matchings into which the edges of a graph G {\displaystyle G} can
Induced_matching
Graph of intervisible locations in computational geometry
visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents
Visibility_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
Sudden population decline in Russia
greater or lesser degree until 2013. When this trend is plotted on a line graph starting from the mid-1980s, the lines cross in 1992, hence the name.
Russian_cross_(demography)
4-regular graph on 6 vertices. Graph equations for line graphs and total graphs, DM Cvetkovic, SK Simic – Discrete Mathematics, 1975 Graph equations, graph inequalities
Graph_equation
Examination of the heart's electrical activity
that shows a line graph of the heart's electrical activity through repeated cardiac cycles. It is an electrogram of the heart which is a graph of voltage
Electrocardiography
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
One of two types of graph
key building blocks of line perfect graphs. The term "book-graph" has been employed for other uses. Barioli used it to mean a graph composed of a number
Book_(graph_theory)
Tree graph with one central node and leaves of length 1
the exceptional cases of the Whitney graph isomorphism theorem: in general, graphs with isomorphic line graphs are themselves isomorphic, with the exception
Star_(graph_theory)
Embedding a graph in 3D space with no cycles interlinked
In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional
Linkless_embedding
Graph where all pairs of vertices are automorphic
regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such
Vertex-transitive_graph
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
Undirected unit-distance graph requiring four colors
line segment has differently-colored endpoints requires at least four colors. The method of construction of the Golomb graph as a unit distance graph
Golomb_graph
Trail in a graph that visits each edge once
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)
Eulerian_path
Type of graph
A bullet graph is a variation of a bar graph developed by Stephen Few. Seemingly inspired by the traditional thermometer charts and progress bars found
Bullet_graph
Graph representing incident points and lines
configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line. They are named for
Levi_graph
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
3-regular graph with no 3-edge-coloring
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three
Snark_(graph_theory)
Point where a function crosses an axis and changes sign
negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathematics
Zero_crossing
Fundamental unit of which graphs are formed
and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless
Vertex_(graph_theory)
Edge-face adjacencies in another graph
graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were
Medial_graph
Matrix that shows the relationship between two classes of objects
graph. The column of a negative edge has either a 1 or a −1 in both rows. The line graph and Kirchhoff matrix properties generalize to signed graphs.
Incidence_matrix
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 in geometry for representing a polygon by a topological skeleton
polygons by Aichholzer et al. (1995), and generalized to planar straight-line graphs (PSLG) by Aichholzer & Aurenhammer (1996). In their interpretation as
Straight_skeleton
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
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
Topics referred to by the same term
concept applicable to normal functions Derivative (graph theory), an alternative term for a line graph Derivative (finance), a contract whose value is derived
Derivative_(disambiguation)
Visual presentation on some surface
computer graphics. Examples are photographs, drawings, line art, mathematical graphs, line graphs, charts, diagrams, typography, numbers, symbols, geometric
Graphics
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
Graph layout on multiple half-planes
half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the spine, and the
Book_embedding
American-born mathematician
Michigan State University to research graph theory. His dissertation was Graphs and Their Associated Line-Graphs. Chartrand worked with Frank Harary at
Gary_Chartrand
Graph drawing with vertices on a line
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane and edges are drawn using
Arc_diagram
In graph theory, the arrangement graph A n , k {\displaystyle A_{n,k}} is a graph defined on the vertex set consisting of all permutations of k {\displaystyle
Arrangement_graph
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Fewest edge crossings in drawing of a graph
graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is
Crossing number (graph theory)
Crossing_number_(graph_theory)
Visualization of node-link graphs
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional
Graph_drawing
Theorem in combinatorics
… , n } {\displaystyle \sigma (i,j)\in \{1,\dots ,n\}} . Orient the line graph as follows: for two cells in the same row, direct the arc from the smaller
Dinitz_theorem
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
travel, tourism, insurance
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travel, tourism, insurance