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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
Area of discrete mathematics
group. Algebraic graph theory also studies the algebraic invariants, chromatic polynomial, Tutte polynomial of a graph, and knot invariant. A graph invariant
Graph_theory
Linear algebra aspects of graph theory
regular graph Algebraic connectivity Algebraic graph theory Spectral clustering Spectral shape analysis Estrada index Lovász theta Expander graph Weisstein
Spectral_graph_theory
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)
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 need
Connectivity_(graph_theory)
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Second-smallest eigenvalue of a graph Laplacian
of a graph, algebraic connectivity ≤ connectivity {\displaystyle {\text{algebraic connectivity}}\leq {\text{connectivity}}} , unless the graph is complete
Algebraic_connectivity
Area of combinatorics
geometries. Algebraic graph theory Combinatorial commutative algebra Polyhedral combinatorics Algebraic Combinatorics (journal) Journal of Algebraic Combinatorics
Algebraic_combinatorics
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
British mathematician
and answers. In 1974, Biggs published Algebraic Graph Theory which articulates properties of graphs in algebraic terms, then works out theorems regarding
Norman_L._Biggs
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)
All even-degree subgraphs of a graph
the graph. The same space can also be described in terms from algebraic topology as the first homology group of the graph. Using homology theory, the
Cycle_space
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
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
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
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
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)
On the number of spanning trees in a graph
mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph. It states
Kirchhoff's_theorem
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
Set of unordered triples from a vertex set
two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs. On the set of vertices
Two-graph
Characteristic of undirected graphs
graph theory, a branch of mathematics, the rank of an undirected graph has two unrelated definitions. Let n equal the number of vertices of the graph
Rank_(graph_theory)
unsolved problems in mathematics Babai's problem is a problem in algebraic graph theory first proposed in 1979 by László Babai. Let G {\displaystyle G}
Babai's_problem
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Mixing property of Markov chains and graphs
In theoretical computer science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time
Conductance_(graph_theory)
Graph where any two nodes of equal distance are isomorphic
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any
Distance-transitive_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
Type of matrix in algebraic graph theory
In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the
Degree_matrix
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 related to another graph by a covering map
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to
Covering_graph
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)
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
spectral graph theory, distributed computing, symbolic dynamics, graph neural networks, and category theory, under different names such as graph divisor
Fibrations_of_graphs
Slovenian mathematician
of Koper. His research focuses on topics in algebraic graph theory, particularly the symmetry of graphs and the action of finite groups on combinatorial
Dragan_Marušič
Maximal subgraph whose vertices can reach each other
ways in graph theory as well. In algebraic graph theory it equals the multiplicity of 0 as an eigenvalue of the Laplacian matrix of a finite graph. It is
Component_(graph_theory)
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
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
Graph property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices
Distance-regular_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 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 defined from a mathematical group
Vertex-transitive graph Generating set of a group Lovász conjecture Cube-connected cycles Algebraic graph theory Cycle graph (algebra) Proof: Let σ : V
Cayley_graph
Study of discrete mathematical structures
parts of topology, e.g. knot theory. Algebraic graph theory has close links with group theory and topological graph theory has close links to topology
Discrete_mathematics
Trail in which only the first and last vertices are equal
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is
Cycle_(graph_theory)
Graph polynomial generating numbers of matchings
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
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
Algebraic structure in network theory
world; the Wang algebra formulation is useful in electrical networks for solving problems involving topological methods, graph theory, and Hamiltonian
Wang_algebra
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
Symmetric function invariant of graphs
function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight generating function for proper graph colorings, and
Chromatic_symmetric_function
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
In graph theory, a branch of mathematics, an equitable partition of the vertex set V of a graph G = (V, E) is a partition of V such that, for any pair
Equitable_partition
Measure of how connected and clustered a node is in its graph
In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most
Clustering_coefficient
British-canadian mathematician
British-Canadian mathematician who worked in algebraic graph theory, group theory, combinatorial design theory, and discrete computational mathematics. He
Leonard_Soicher
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Algebraic encoding of graph connectivity
G} . Though originally studied in algebraic graph theory as a generalization of counting problems related to graph coloring and nowhere-zero flow, it
Tutte_polynomial
studied and generalized in graph theory, in part because of its elegant proof using techniques from algebraic graph theory. More strongly, Aigner & Ziegler
Graham–Pollak_theorem
theorem (graph theory) Nicomachus's theorem (number theory) Ore's theorem (graph theory) Paley's theorem (algebra) Perfect graph theorem (graph theory) Perlis
List_of_theorems
Mathematical finite graph-associated function
{\displaystyle p} on G {\displaystyle G} (known in graph theory as a "reduced closed walk"; it is not a graph geodesic) is a finite sequence of vertices p =
Ihara_zeta_function
Special case of a strongly regular graph
of graph theory, a conference graph is a strongly regular graph with parameters v, k = (v − 1)/2, λ = (v − 5)/4, and μ = (v − 1)/4. It is the graph associated
Conference_graph
Graph where all pairs of edges are automorphic
In the mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism
Edge-transitive_graph
In the mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and
Edge_and_vertex_spaces
Mathematical Graph
In graph theory, a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself
Walk-regular_graph
Graph with nodes connected in a closed chain
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if
Cycle_graph
Clustering methods
of graphs and computer logic based on eigenvectors of connections matrices". IBM Technical Disclosure Bulletin. Fiedler, Miroslav (1973). "Algebraic connectivity
Spectral_clustering
Branch of mathematics
associative Outline of algebra Representation theory – Branch of mathematics that studies abstract algebraic structures Tensor – Algebraic object with geometric
Algebra
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
Boolean algebra De Morgan algebra First-order logic Heyting algebra Lindenbaum–Tarski algebra Skew Boolean algebra Algebraic normal form Boolean conjunctive
List of Boolean algebra topics
List_of_Boolean_algebra_topics
In the mathematical field of spectral graph theory, Brouwer's conjecture is a conjecture by Andries Brouwer on upper bounds for the intermediate sums of
Brouwer's_conjecture
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Undirected, connected, and acyclic graph
In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected
Tree_(graph_theory)
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
mathematical field of graph theory, a core is a notion that describes behavior of a graph with respect to graph homomorphisms. Graph C {\displaystyle C}
Core_(graph_theory)
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
American mathematician
specializing in graph theory. She is a professor of mathematics at Western Michigan University and the author of many textbooks on graph theory and mathematical
Ping_Zhang_(graph_theorist)
Topics referred to by the same term
(category theory), a generalization of mathematical products Fibre product or pullback Coproduct or pushout Wick product of random variables Graph product
Product
is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts the number of
Order_polynomial
On cycle bases of planar graphs
In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who
Mac Lane's planarity criterion
Mac_Lane's_planarity_criterion
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
2003 mathematics text
Elementary Number Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible to
Elementary Number Theory, Group Theory and Ramanujan Graphs
Elementary_Number_Theory,_Group_Theory_and_Ramanujan_Graphs
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
popular textbook on algebraic graph theory, entitled Algebraic Graph Theory, with Gordon Royle, His earlier textbook on algebraic combinatorics discussed
Chris_Godsil
Flow graph invented by Claude Shannon
linear algebraic equations. This problem, usually solved by matrix methods, can also be solved via graph theory. " Deo, Narsingh (1974). Graph Theory with
Signal-flow_graph
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
formulation of Kalman's criterion with tools from algebraic graph theory via the minimum rank of a graph and related notions. Controllability Gramian Sharma
Network_controllability
An object whose endomorphisms are isomorphic to another structure
uses deprecated parameter |citeseerx= (help) Biggs, Norman (1994), Algebraic Graph Theory, Cambridge Mathematical Library, Cambridge University Press,
Representation_(mathematics)
Cycles in a graph that generate all cycles
In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the
Cycle_basis
Australian mathematician
Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs. Cheryl Elisabeth Praeger was born
Cheryl_Praeger
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)
Function of a matrix
hafnian counts perfect matchings in a graph from its adjacency matrix, the permanent counts matchings in a bipartite graph from its biadjacency matrix. The
Hafnian
Matrix that shows the relationship between two classes of objects
common graph representation in graph theory. It is different to an adjacency matrix, which encodes the relation of vertex-vertex pairs. In graph theory an
Incidence_matrix
Matrix in math with special properties
matrix, the matrix S can be viewed as the Seidel adjacency matrix of a graph. The graph has n − 1 vertices, corresponding to the rows and columns of S, and
Conference_matrix
Branch of discrete mathematics
century) helped lay the foundation for enumerative and algebraic combinatorics. Graph theory also enjoyed an increase of interest at the same time, especially
Combinatorics
Concept in graph theory and network analysis
In graph theory and network analysis, group centrality generalizes the concept of centrality to sets of nodes in a network. Introduced by Everett and Borgatti
Group_centrality
Geometric graph with unit edge lengths
In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting
Unit_distance_graph
Graph that is edge-transitive and regular but not vertex-transitive
graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is
Semi-symmetric_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)
Graph with nodes connected linearly
In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that
Path_graph
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
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
the context of spectral graph theory. More precisely, let G be a graph with n vertices. It is assumed that G is a simple graph, that is, it does not contain
Graph_energy
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