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Class of undirected graphs defined from systems of sets
In 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
Graph whose vertices correspond to combinations of a set of n elements
In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements
Kneser_graph
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
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
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
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
Class of simple graphs defined from vector spaces
Grassmann graphs are q-analogs of the parameters of Johnson graphs, and Grassmann graphs have several of the same graph properties as Johnson graphs. Jq(n
Grassmann_graph
In polytope theory, the edge graph (also known as vertex-edge graph or just graph) of a polytope is a combinatorial graph whose vertices and edges correspond
Graph_of_a_polytope
Graph where any two nodes of equal distance are isomorphic
distance-transitive graphs, especially of those whose diameter is 2. Some first examples of families of distance-transitive graphs include: The Johnson graphs. The Grassmann
Distance-transitive_graph
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
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Method to find shortest paths
Johnson's algorithm is a way to find the shortest paths between all pairs of vertices in an edge-weighted directed graph. It allows some of the edge weights
Johnson's_algorithm
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
Upper bound on intersecting set families
theorem. The corresponding graph-theoretic formulation of this generalization involves Johnson graphs in place of Kneser graphs. For large enough values
Erdős–Ko–Rado_theorem
Subgraph induced by all nodes linked to a given node of a graph
In graph theory, the neighbourhood of a vertex v in a graph G is the subgraph of G induced by all the vertices that are connected to v by an edge (vertices
Neighbourhood_(graph_theory)
Graph able to be partitioned into multiple independent sets
In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently
Multipartite_graph
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first
Complete_bipartite_graph
Graph whose edges are given independent directions at both ends
In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) is a graph in which each edge is given an independent
Bidirected_graph
Unsolved problem in computational complexity theory
computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem is
Graph_isomorphism_problem
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
Two pentagonal pyramids fused base-to-base
give rise to a graph. It is one of the four four-connected simplicial well-covered graphs. It is also one of the six connected graphs in which its neighborhood
Pentagonal_bipyramid
Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Hungarian-American mathematician and computer scientist
canonical partitioning techniques. We show that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioning. In 1988
László_Babai
Convex polyhedron with 14 triangle faces
composite polyhedron, and Johnson solid. The edges and vertices of the triaugmented triangular prism form a maximal planar graph with 9 vertices and 21 edges
Triaugmented_triangular_prism
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Family of graphs with 2n nodes and n(n-1) edges
In graph theory, a branch of mathematics, a crown graph on 2n vertices is an undirected graph with two sets of vertices {u1, u2, …, un} and {v1, v2, …
Crown_graph
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Quantum algorithm
marked node in a graph. The concept of a quantum walk is inspired by classical random walks, in which a walker moves randomly through a graph or lattice. In
Quantum_walk_search
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)
{\tbinom {d}{k}}} . The vertex-edge graph of the hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is the Johnson graph J ( d , k ) {\displaystyle J(d,k)}
Hypersimplex
Path in a graph that visits each vertex exactly once
the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly
Hamiltonian_path
Archimedean solid with 62 faces
pentagrammic prisms. In the mathematical field of graph theory, a rhombicosidodecahedral graph is the graph of vertices and edges of the rhombicosidodecahedron
Rhombicosidodecahedron
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)
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
AL19. Garey & Johnson (1979), AL21. Antonio Lozano and Jose L. Balcazar. The complexity of graph problems for succinctly represented graphs. In Manfred
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Prism with a 3-sided base
a family, the graph of a triangular prism is the prism graph Π3, where the symbol Πn represents the graph of an n-sided prism. The graph of a triangular
Triangular_prism
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
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
Graph path which is an induced subgraph
In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence
Induced_path
Archimedean solid with 8 faces
World Cup. In the mathematical field of graph theory, a truncated tetrahedral graph is an Archimedean graph, the graph of vertices and edges of the truncated
Truncated_tetrahedron
Formula to quantify column buckling under a given load
relatively short length compared to their cross section), the graph will follow the Johnson parabola; in contrast, larger slenderness values will align
Johnson's_parabolic_formula
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
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)
Graph made from a subset of another graph's nodes and their edges
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges, from the original
Induced_subgraph
NP-hard problem in combinatorial optimization
version of the TSP (where given a length L, the task is to decide whether the graph has a tour whose length is at most L) belongs to the class of NP-complete
Travelling_salesman_problem
British political scandal
restrictions prohibited most gatherings. The scandal contributed to Boris Johnson's downfall as Prime Minister and his resignation as an MP. While several
Partygate
Polyhedron resembling a soccerball
represented as a polyhedral graph, meaning a planar graph (one that can be drawn without crossing edges) and 3-vertex-connected graph (remaining connected whenever
Truncated_icosahedron
Intersection graph of unit disks in the plane
geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex
Unit_disk_graph
Task of computing complete subgraphs
vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what
Clique_problem
Two tetrahedra joined by one face
a graph can be represented as the skeleton of a polyhedron if it is a planar (can be drawn without crossing any edges) and three-connected graph (it
Triangular_bipyramid
Archimedean solid with 62 faces
the mathematical field of graph theory, a truncated icosidodecahedral graph (or great rhombicosidodecahedral graph) is the graph of vertices and edges of
Truncated_icosidodecahedron
Node labeling problem in graph theory
In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number
Graph_bandwidth
Unrelated vertices in graphs
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a
Independent set (graph theory)
Independent_set_(graph_theory)
Partition of a graph's nodes into cliques
In graph theory, a clique cover or partition into cliques of a given undirected graph is a collection of cliques that cover the whole graph. Generally
Clique_cover
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
comprehensive. Many problems of this type can be found in Garey & Johnson (1979). Graphs occur frequently in everyday applications. Examples include biological
List_of_NP-complete_problems
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
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
1979 classic textbook on computational complexity theory
are: Graph isomorphism This problem is known to be in NP, but it is unknown if it is NP-complete. Subgraph homeomorphism (for a fixed graph H) Graph genus
Computers_and_Intractability
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
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
Gluing graphs at complete subgraphs
In graph theory, a branch of mathematics, a clique sum (or clique-sum) is a way of combining two graphs by gluing them together at a clique, analogous
Clique-sum
American political campaign
The 1964 presidential campaign of Lyndon B. Johnson was a successful campaign for Johnson and his running mate Hubert Humphrey for their election as president
Lyndon B. Johnson 1964 presidential campaign
Lyndon_B._Johnson_1964_presidential_campaign
Subset of a graph's vertices, including at least one endpoint of every edge
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In
Vertex_cover
In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and
Topological_graph
Sliding puzzle with fifteen pieces and one space
showed that other than one exceptional graph on 7 vertices, it is possible to obtain all permutations unless the graph is bipartite, in which case exactly
15_puzzle
Dimensionality reduction of graph-based semantic data objects [machine learning task]
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine
Knowledge_graph_embedding
Tree which includes all vertices of a graph
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may
Spanning_tree
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
Vertices whose removal breaks all cycles
mathematical discipline of graph theory, a feedback vertex set (FVS) of a graph is a set of vertices whose removal leaves a graph without cycles ("removal"
Feedback_vertex_set
Graph which remains connected when fewer than k edges are removed
graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph
Edge_connectivity
Archimedean solid with 32 faces
graph. The truncated dodecahedron can be applied in the polyhedron's construction known as the augmentation. Examples of polyhedrons are the Johnson solids
Truncated_dodecahedron
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
American mathematician (1916–1996)
the Ford–Johnson algorithm for sorting, which for 20 years was the comparison sort with the minimum known number of comparisons. Johnson graphs and the
Selmer_M._Johnson
Vertex adjacent to all others in a graph
In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating
Universal_vertex
Mathematical result
applications in compressed sensing, manifold learning, dimensionality reduction, graph embedding, and natural language processing. Much of the data stored and
Johnson–Lindenstrauss_lemma
Partition of a graph by removing fewest possible edges
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some
Minimum_cut
Finding shortest walks through all graph edges
In graph theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find
Chinese_postman_problem
Subset of a graph's edges
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is an endpoint of at least one edge of the set. In computer
Edge_cover
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
Operation on graphs
In graph theory, ΔY- and YΔ-transformations (also written delta-wye and wye-delta) are a pair of operations on graphs. A ΔY-transformation replaces a triangle
YΔ-_and_ΔY-transformation
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
mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of
Vertex_cycle_cover
On short connecting nets with added points
term Steiner tree problem, is the Steiner tree problem in graphs. Given an undirected graph with non-negative edge weights and a subset of vertices, usually
Steiner_tree_problem
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
The vertical composite HG is the anchored graph defined by the following data: (1) The connected plane graph of HG is the quotient G ⊔ H { c o d G = d
Pasting_theorem
In graph theory and theoretical computer science, the monochromatic triangle problem is an algorithmic problem on graphs, in which the goal is to partition
Monochromatic_triangle
Solid with 12 equal pentagonal faces
represented as a graph, and it is called the dodecahedral graph, a Platonic graph. This graph can also be constructed as the generalized Petersen graph G ( 10
Regular_dodecahedron
Operation in Euclidean geometry
polyhedron notation uses a for ambo as this operator. In graph theory this operation creates a medial graph. The rectification of any regular self-dual polyhedron
Rectification_(geometry)
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
11th Johnson solid (16 faces)
the icosahedral graph's vertices, leaving 11 vertices, an odd number, resulting in a graph with a perfect matching. Hence, the graph is a 2-vertex connected
Gyroelongated pentagonal pyramid
Gyroelongated_pentagonal_pyramid
Method of graph decomposition
In graph theory, a bramble for an undirected graph G is a family of connected subgraphs of G that all touch each other: for every pair of disjoint subgraphs
Bramble_(graph_theory)
Method for finding minimum spanning trees
algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes
Prim's_algorithm
Archimedean solid with 32 faces
represented as the symmetric graph with 30 vertices and 60 edges, one of the Archimedean graphs. It is a symmetric quartic graph, meaning that each vertex
Icosidodecahedron
Polyhedron with eight triangular faces
(1993). "Generating all 3-connected 4-regular planar graphs from the octahedron graph". Journal of Graph Theory. 17 (5): 613–620. doi:10.1002/jgt.3190170508
Octahedron
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
Geometry problem on tiling by hypercubes
Brakensiek et al. (2020). Hartnett (2020). Johnson & Trick (1996); Debroni et al. (2011), "Keller graphs are in the benchmark set of clique problems
Keller's_conjecture
Matrix with every entry equal to one
application of algebraic methods to graph theory. For example, if A is the adjacency matrix of an n-vertex undirected graph G, and J is the all-ones matrix
Matrix_of_ones
Theorem that every subgroup of a free group is itself free
infinite) topological graph, the Schreier coset graph having one vertex for each coset in G/H. In any connected topological graph, it is possible to shrink
Nielsen–Schreier_theorem
JOHNSON GRAPH
JOHNSON GRAPH
Surname or Lastname
English
English : habitational name from Wonson, Devon.
Surname or Lastname
English
English : unexplained. Compare Dunson, of which this may be a variant.
Surname or Lastname
English
English : patronymic from John.Respelling of Swedish Jonsson.
Boy/Male
French American English Scottish
Jehovah has been gracious; has shown favor.
Boy/Male
English
Son of Happiness Joy
Boy/Male
British, English, Scottish
Son of John; From John's Farm
Surname or Lastname
English
English : unexplained.Swiss French (Vaud) : unexplained.German : unexplained.
Surname or Lastname
English
English : from a pet form of John.
Surname or Lastname
English
English : from a pet form of John, with the Middle English suffix -cok (see Cocke).
Surname or Lastname
English
English : patronymic from a reduced form of Rowland.
Boy/Male
British, English
Son of John
Girl/Female
Hindu
Boy/Male
Scandinavian
Hebrew John 'Jehovah has been gracious; has shown favor.
Surname or Lastname
English and Scottish
English and Scottish : patronymic from the personal name John. As an American family name, Johnson has absorbed patronymics and many other derivatives of this name in continental European languages. (For forms, see Hanks and Hodges 1988.)Johnson is the second most frequent surname in the U.S. It was brought independently to North America by many different bearers from the 17th and 18th centuries onward.
Surname or Lastname
English
English : patronymic from a pet form of the personal name Thomas.
Surname or Lastname
English
English : patronymic from Job.
Boy/Male
Scottish
From John's farm.
Surname or Lastname
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Boy/Male
American, Australian, British, Chinese, Christian, English, French, Hebrew, Indian, Scottish, Tamil
Son of John; Variant of the John
Surname or Lastname
Americanized spelling of Jansen, Janssen, and Jansson.English
Americanized spelling of Jansen, Janssen, and Jansson.English : patronymic from the personal name Jan, a medieval form of John.
JOHNSON GRAPH
JOHNSON GRAPH
Girl/Female
Biblical
Milk, fatness.
Female
French
Feminine form of French Benoît, BENOÎTE means "blessed."
Boy/Male
Hindu, Indian, Marathi
Lord Vishnu
Boy/Male
Scottish
From the peninsula.
Boy/Male
Teutonic Swedish
Lion.
Surname or Lastname
English
English : variant spelling of Heap.German : variant of Heeb.
Girl/Female
Tamil
Soft
Boy/Male
Indian
Gods warrior
Girl/Female
Muslim/Islamic
Dew
Boy/Male
Indian, Punjabi, Sikh
Lord's Lotus
JOHNSON GRAPH
JOHNSON GRAPH
JOHNSON GRAPH
JOHNSON GRAPH
JOHNSON GRAPH
a.
Pertaining to or resembling Dr. Johnson or his style; pompous; inflated.
n.
A history of the acts and events of a life; a biography; as, Johnson wrote the life of Milton.
n.
A rotating wheel, mounted in a ring or rings, for illustrating the dynamics of rotating bodies, the composition of rotations, etc. It was devised by Professor W. R. Johnson, in 1832, by whom it was called the rotascope.
adv.
In a graphic manner; vividly.
n.
The quality or state of being graphic.
n.
A genus of grasses, properly limited to two species, Sorghum Halepense, the Arabian millet, or Johnson grass (see Johnson grass), and S. vulgare, the Indian millet (see Indian millet, under Indian).
a.
Resembling graphite or plumbago.
a.
Alt. of Graphitoidal
n.
Alt. of Graphicalness
a.
Alt. of Graphical
a.
Relating to, or characteristic of, Boswell, the biographer of Dr. Johnson.
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
n.
A manner of acting or of writing peculiar to, or characteristic of, Dr. Johnson.
n.
The literary style of Dr. Samuel Johnson, or one formed in imitation of it; an inflated, stilted, or pompous style, affecting classical words.
n.
A comparison made; elaborate tracing of similarity; as, Johnson's parallel between Dryden and Pope.
n.
A modification of the father's name borne by the son; a name derived from that of a parent or ancestor; as, Pelides, the son of Peleus; Johnson, the son of John; Macdonald, the son of Donald; Paulowitz, the son of Paul; also, the surname of a family; the family name.
n.
See Graphoscope.
a.
Pertaining to, containing, derived from, or resembling, graphite.