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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
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
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
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
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
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)
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
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
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
{\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
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)
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
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)
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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)
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
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
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)
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
field of graph theory, an integral graph is a graph whose adjacency matrix's spectrum consists entirely of integers. In other words, a graph is an integral
Integral_graph
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Regular graph with girth more than twice its diameter
mathematics 🝃 More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth (the shortest cycle length) is more than
Moore_graph
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
theorem (graph theory) Binomial theorem (algebra, combinatorics) Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Brooks's
List_of_theorems
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
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
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
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
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
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
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)
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
Study of categorified structures
higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra. A first
Higher-dimensional_algebra
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
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
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
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
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
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
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
If the algebra has the property that every interval is finite, then this graph is a median graph, and it accurately represents the algebra in that the
Median_algebra
Set of unordered triples from a vertex set
the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been
Two-graph
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
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)
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)
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)
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
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
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
One of two types of graph
graphs". Linear Algebra and Its Applications. 420 (2–3): 526–9. doi:10.1016/j.laa.2006.08.007. Erdős, Paul (1963). "On the structure of linear graphs"
Book_(graph_theory)
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
All even-degree subgraphs of a graph
number, of the graph. The same space can also be described in terms from algebraic topology as the first homology group of the graph. Using homology
Cycle_space
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)
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
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)
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
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
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)
Type of knowledge base
algebras on the graph. In subsequent decades, the distinction between semantic networks and knowledge graphs was blurred. Some early knowledge graphs
Knowledge_graph
Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
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
On graphs with given symmetry groups
Frucht's theorem is a result in algebraic graph theory, conjectured by Dénes Kőnig in 1936 and proved by Robert Frucht in 1939. It states that every finite
Frucht's_theorem
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
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
Algebraic signal processing (ASP) is an emerging area of theoretical signal processing (SP). In the algebraic theory of signal processing, a set of filters
Algebraic_signal_processing
Tayfeh-Rezaie, B. (2010). "On the sum of Laplacian eigenvalues of graphs". Linear Algebra and Its Applications. 432 (9): 2214–2221. doi:10.1016/j.laa.2009
Brouwer's_conjecture
4-regular undirected graph in mathematics
In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after
Robertson_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
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
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
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
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