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especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by
Graph_algebra
Branch of mathematics
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatorial
Algebraic_graph_theory
Second-smallest eigenvalue of a graph Laplacian
The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting
Algebraic_connectivity
a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz algebras and
Graph_C*-algebra
Graph with nodes connected in a closed chain
related to Cycle graphs. Complete bipartite graph Complete graph Circulant graph Cycle graph (algebra) Null graph Path graph Some simple graph spectra. win
Cycle_graph
Area of discrete mathematics
invariants" and "co-variants" of algebra and molecular diagrams. The definition of a graph can vary, but one can understand that a graph is a structure consisting
Graph_theory
Graph structure studied in group theory
In group theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given
Cycle_graph_(algebra)
Directed path algebra
path algebra is an algebra constructed from a directed graph. Leavitt path algebras generalize Leavitt algebras and may be considered as algebraic analogues
Leavitt_path_algebra
API for graph data and graph operations
GraphBLAS (/ˈɡræfˌblɑːz/ ) is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. GraphBLAS
GraphBLAS
Linear algebra aspects of graph theory
its eigenvalues are real algebraic integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not
Spectral_graph_theory
Graph where any two nodes of equal distance are isomorphic
"Distance-Transitive Graphs", Algebraic Graph Theory, New York: Springer-Verlag, pp. 66–69, section 4.5. Ivanov, A. A. (1992), "Distance-transitive graphs and their
Distance-transitive_graph
{\displaystyle C^{*}} -algebras of k {\displaystyle k} -graphs. There is also a close relationship between k {\displaystyle k} -graphs and strict factorization
K-graph_C*-algebra
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Spectral graph theory concept
Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly
Ramanujan_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
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
Electronic calculator capable of plotting graphs
following in 1988, and Texas Instruments in 1990. Some graphing calculators have a computer algebra system (CAS), which means that they are capable of producing
Graphing_calculator
Universal C*-algebra
Cuntz algebras have been generalised in many ways. Notable amongst which are the Cuntz–Krieger algebras, graph C*-algebras and k-graph C*-algebras. In signal
Cuntz_algebra
Square matrix used to represent a graph or network
not allowed in simple graphs. It is also sometimes useful in algebraic graph theory to replace the nonzero elements with algebraic variables. The same concept
Adjacency_matrix
Index of articles associated with the same name
theory: Cyclic function, a periodic function Cycle graph, a connected, 2-regular graph Cycle graph (algebra), a diagram representing the cycles determined
Cyclic_(mathematics)
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Index of articles associated with the same name
in graphs Other similarly-named concepts include Cycle graph (algebra), a graph that illustrates the cyclic subgroups of a group Circulant graph, a graph
Cyclic_graph
Graph algebra is systems-centric modeling tool for the social sciences. It was first developed by Sprague, Pzeworski, and Cortes as a hybridized version
Graph algebra (social sciences)
Graph_algebra_(social_sciences)
query Canonical form (Boolean algebra) Conjunctive normal form Disjunctive normal form Formal system And-inverter graph Logic gate Boolean analysis Boolean
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Theory of algebraic structures in general
universal algebra. Mathematics portal Equational logic Graph algebra Term algebra Clone Universal algebraic geometry Simple algebra (universal algebra) Higgins
Universal_algebra
Topological algebra associated to continuous groups
Graph algebra Incidence algebra Hecke algebra of a locally compact group Path algebra Groupoid algebra Stereotype algebra Stereotype group algebra Hopf
Group algebra of a locally compact group
Group_algebra_of_a_locally_compact_group
Geometric graph with unit edge lengths
unit distance graph can be colored with seven colors. For every algebraic number α , {\displaystyle \alpha ,} there is a unit distance graph with two vertices
Unit_distance_graph
Creating a new graph from an existing graph
also another algebraic-like approach to graph rewriting, based mainly on Boolean algebra and an algebra of matrices, called matrix graph grammars. Yet
Graph_rewriting
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Associative algebra used in combinatorics
In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative
Incidence_algebra
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
Characteristic of undirected graphs
J., Domke, Gayla S., Miller, Valerie A. (1997), The rank of a graph after vertex addition. Linear Algebra and its Applications, vol. 265, pp. 55–69.
Rank_(graph_theory)
Study of discrete mathematical structures
Algebraic graph theory has close links with group theory and topological graph theory has close links to topology. There are also continuous graphs;
Discrete_mathematics
Directed graph which is also a multigraph
Assembly theory Graph algebra Group ring Incidence algebra Quiver diagram Semi-invariant of a quiver Toric variety Derived noncommutative algebraic geometry
Quiver_(mathematics)
Pictorial representation of symmetry
graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras over
Dynkin_diagram
Type of knowledge base
Knowledge Graphs, focusing on the design of semantic networks with edges restricted to a limited set of relations, to facilitate algebras on the graph. In subsequent
Knowledge_graph
pp. 6-7. These C*-algebras were created in order to simultaneously generalize the classes of graph C*-algebras and Exel–Laca algebras, giving a unified
Ultragraph_C*-algebra
Graph where all pairs of vertices are automorphic
Edge-transitive graph Lovász conjecture Semi-symmetric graph Zero-symmetric graph Godsil, Chris; Royle, Gordon (2013) [2001], Algebraic Graph Theory, Graduate
Vertex-transitive_graph
Series of Casio graphing calculators
The Casio Algebra FX series was a line of graphing calculators manufactured by Japanese electronics company Casio Computer Co., Ltd from 1999 to 2003.
Casio_Algebra_FX_Series
Graph representing connectivity between cliques of another graph
the complement graph of a path graph is a Fibonacci cube. The complete subgraphs of G can be given the structure of a median algebra: the median of three
Simplex_graph
Graph in which all ordered pairs of linked nodes are automorphic
graphs of degree 3 or more for t ≥ 8. In the case of the degree being exactly 3 (cubic symmetric graphs), there are none for t ≥ 6. Algebraic graph theory
Symmetric_graph
Algebraic structure in network theory
generating the trees of a graph. The Wang algebra formulation has been used to systematically generate King-Altman directed graph patterns. Such patterns
Wang_algebra
Writing paper with a grid
Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available
Graph_paper
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
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an example
Adjacency_algebra
Algebra based on a vector space with a quadratic form
mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure
Clifford_algebra
Graph with nodes connected linearly
example, Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). In algebra, path graphs appear as the Dynkin diagrams of type A. As such, they classify the
Path_graph
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Type of diagrammatic notation for propositional logic
beta graphs). Peirce proposed three systems of existential graphs: alpha, isomorphic to propositional logic and the two-element Boolean algebra; beta
Existential_graph
Linear map or polynomial function of degree one
notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero (a constant
Linear_function
Mathematical Graph
vertex-transitive graphs are walk-regular. The distance-regular graphs are walk-regular. More generally, any simple graph in a homogeneous coherent algebra is walk-regular
Walk-regular_graph
Branch of discrete mathematics
20th century) helped lay the foundation for enumerative and algebraic combinatorics. Graph theory also enjoyed an increase of interest at the same time
Combinatorics
Area of combinatorics
combinatorial objects of interest in algebraic combinatorics either admitted much symmetry (association schemes, strongly regular graphs, posets with a group action)
Algebraic_combinatorics
Idempotent semiring endowed with a closure operator
In mathematics and theoretical computer science, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes
Kleene_algebra
Series of graphing calculators
graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system
TI-89_series
Graph where each vertex has the same number of neighbors
graphs : a graph is connected and regular if and only if the matrix of ones J, with J i j = 1 {\displaystyle J_{ij}=1} , is in the adjacency algebra of
Regular_graph
Undirected graph defined from a group
In the mathematics of graph theory and finite groups, a prime graph is an undirected graph defined from a group. These graphs were introduced in a 1981
Prime_graph
theorem (graph theory) Binomial theorem (algebra, combinatorics) Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Brooks's
List_of_theorems
Trail in which only the first and last vertices are equal
cycles. A cycle basis of the graph is a set of simple cycles that forms a basis of the cycle space. Using ideas from algebraic topology, the binary cycle
Cycle_(graph_theory)
Adjacent subset of an undirected graph
graph G and an edge connecting two cliques that differ by a single vertex. It is an example of median graph, and is associated with a median algebra on
Clique_(graph_theory)
Commuting graphs have been used to study groups and semigroups by seeking relationships between the combinatorial structure of the graph and the algebraic structure
Commuting_graph
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
function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumeration problem) or asymptotically. The
Graph_enumeration
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Ring that is also a vector space or a module
A quiver algebra (or a path algebra) of a directed graph is the free associative algebra over a field generated by the paths in the graph. Given any
Associative_algebra
Graph of a dynamical system
In mathematics, a Bratteli diagram is a combinatorial structure: a graph composed of vertices labelled by positive integers ("level") and unoriented edges
Bratteli_diagram
American political scientist
Theories (1995) Differential Equations: A Modeling Approach (2007) Graph Algebra: Mathematical Modeling With a Systems Approach (2007) The Nazi Vote:
Courtney Brown (social scientist)
Courtney_Brown_(social_scientist)
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
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
Mathematical function
whose graph is the top half of the standard unit circle. This function satisfies x 2 + f ( x ) 2 − 1 = 0 {\displaystyle x^{2}+f(x)^{2}-1=0} . Algebraic functions
Algebraic_function
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
Graph of zero divisors of a commutative ring
and more specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring
Zero-divisor_graph
Polynomial whose roots are the eigenvalues of a matrix
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues
Characteristic_polynomial
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
Basic concept of graph theory
a graph is connected". SIAM Journal on Computing. 12 (4): 777–788. doi:10.1137/0212053. MR 0721012.. Godsil, C.; Royle, G. (2001). Algebraic Graph Theory
Connectivity_(graph_theory)
Path in a graph that visits each vertex exactly once
Hamiltonian cycle in the edge graph of the dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structure based on roots of
Hamiltonian_path
Family of triangle-free circulant graphs
(2013) [2001]. "§6.10–6.12: The Andrásfai Graphs—Andrásfai Coloring Graphs, A Characterization". Algebraic Graph Theory. Graduate Texts in Mathematics. Vol
Andrásfai_graph
Product of a number by itself
an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions
Square_(algebra)
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
Algebraic structure modeling logical operations
algebra) Complete Boolean algebra De Morgan's laws Forcing (mathematics) Free Boolean algebra Heyting algebra Hypercube graph Karnaugh map Laws of Form
Boolean_algebra_(structure)
American mathematician
algebras as algebraic analogues of the graph C*-algebras. The Leavitt path algebras are so-named because they are constructed from the path algebra of
Gene_Abrams
Method to convey chess moves
Algebraic notation is the standard method of chess notation, used for recording and describing moves. It is based on a system of coordinates to uniquely
Algebraic_notation_(chess)
Function in algebraic graph theory
chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function
Chromatic_polynomial
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
repeatedly studied and generalized in graph theory, in part because of its elegant proof using techniques from algebraic graph theory. More strongly, Aigner &
Graham–Pollak_theorem
Type of graph in graph theory
1-Transitive Graphs". Canadian Mathematical Bulletin. 13 (2): 231–237. doi:10.4153/CMB-1970-047-8. Biggs, Norman (1993). Algebraic Graph Theory (2nd ed
Half-transitive_graph
In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space
Graph_homology
Computer algebra system
for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics
SageMath
Czech mathematician (1926–2015)
his contributions to linear algebra, graph theory and algebraic graph theory. His article, "Algebraic Connectivity of Graphs", published in the Czechoslovak
Miroslav_Fiedler
Structure-preserving correspondence between node-link graphs
rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The
Graph_homomorphism
Heuristic test for graph isomorphism
Weisfeiler, B. Yu.; Leman, A. A. (1968). "A Reduction of a Graph to a Canonical Form and an Algebra Arising during This Reduction" (PDF). Nauchno-Technicheskaya
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
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
1–22, MR 0525890. Gutman, Ivan (2001), "The energy of a graph: old and new results", Algebraic combinatorics and applications (Gößweinstein, 1999), Berlin:
Graph_energy
Graph polynomial generating numbers of matchings
numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory. Several different types of matching
Matching_polynomial
American mathematician
the Algebras and Rings in Colorado Springs (ARCS) center. Tomforde has researched the related areas of graph C*-algebras and Leavitt path algebras. With
Mark_Tomforde
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
Number of "holes" of a surface
undirected) Cayley graph for G. The graph genus problem is NP-complete. There are two related definitions of genus of any projective algebraic scheme X {\displaystyle
Genus_(mathematics)
GRAPH ALGEBRA
GRAPH ALGEBRA
Girl/Female
Muslim
Grape like
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Biblical
a grape; a knot
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Boy/Male
Arabic, Modern
Grape
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Hindu
Grape, Belonging to kashmir
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Boy/Male
Indian
Grape
Girl/Female
Indian
Grape vine
Boy/Male
Muslim
Grape
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Indian
Grape like
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Muslim
Grape vine
GRAPH ALGEBRA
GRAPH ALGEBRA
Boy/Male
Muslim
Covered, A title of the prophet
Surname or Lastname
English
English : occupational name for someone who did piece-work (especially someone who threshed grain), from an agent derivative of Anglo-Norman French tasque ‘task’ (Old French tasche, Late Latin taxa, of uncertain origin).Slovenian (Tašker) : unexplained.
Boy/Male
Indian
Brilliant, Majestic, Exalted
Boy/Male
Arabic, Hindu, Indian, Muslim, Sindhi
The Moon of the Faith
Surname or Lastname
English
English : unexplained.
Boy/Male
Sikh
One in equipoise and tranquillity
Girl/Female
Indian
Devotee of Goddess Durga
Girl/Female
Hindu, Indian, Marathi
The Lord of the Earth
Girl/Female
Arabic
Ship
Girl/Female
Latin
Graced with God's bounty.
GRAPH ALGEBRA
GRAPH ALGEBRA
GRAPH ALGEBRA
GRAPH ALGEBRA
GRAPH ALGEBRA
n.
A grape, or a bunch of grapes.
n.
Grapeshot.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
a.
Composed of, or resembling, grapes.
n.
A seed of the grape.
n.
A plant of the genus Muscari; grape hyacinth.
a.
Resembling a grape.
n.
A grape dried in the sun; a raisin.
n.
A mangy tumor on the leg of a horse.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
n.
A variety of shaddock, called also grape fruit.
n.
A grape of many varieties and colors.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.
n.
The cultivation of the vine; grape growing.
a.
Full of small kernels like a grape.
n.
A sort of grape.
n.
The plant which bears this fruit; the grapevine.
n.
A white grape, esteemed for the table.