Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric...
7 KB (671 words) - 16:56, 27 November 2023
mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...
52 KB (6,403 words) - 06:09, 18 June 2024
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...
15 KB (1,825 words) - 10:14, 23 April 2024
finite geometries. Algebraic graph theory Combinatorial commutative algebra Algebraic Combinatorics (journal) Journal of Algebraic Combinatorics Polyhedral...
13 KB (1,286 words) - 17:04, 6 July 2024
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...
51 KB (6,580 words) - 02:26, 3 January 2024
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...
17 KB (2,062 words) - 09:56, 10 July 2024
Adjacency matrix (redirect from Adjacency matrix of a bipartite graph)
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...
20 KB (2,461 words) - 21:32, 22 July 2024
the algebraic connectivity can be negative for general directed graphs, even if G is a connected graph. Furthermore, the value of the algebraic connectivity...
8 KB (970 words) - 06:39, 11 June 2024
Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly...
19 KB (2,689 words) - 01:42, 4 January 2024
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...
10 KB (1,132 words) - 22:12, 9 January 2024
algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory...
190 KB (19,539 words) - 19:39, 10 August 2024
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...
14 KB (1,728 words) - 03:52, 22 May 2024
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...
28 KB (3,689 words) - 23:54, 26 July 2024
Incidence matrix (redirect from Incidence (graph theory))
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...
9 KB (1,278 words) - 15:48, 12 September 2022
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...
6 KB (622 words) - 12:35, 5 October 2023
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...
30 KB (3,441 words) - 12:55, 5 July 2024
In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of...
11 KB (1,158 words) - 12:55, 15 May 2023
Norman L. Biggs (section Algebraic Graph Theory)
and answers. In 1974, Biggs published Algebraic Graph Theory which articulates properties of graphs in algebraic terms, then works out theorems regarding...
12 KB (1,315 words) - 05:05, 10 January 2024
Laplacian matrix (redirect from Kirchhoff matrix (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...
43 KB (4,942 words) - 19:17, 8 July 2024
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...
29 KB (3,553 words) - 00:07, 29 May 2024
Discrete mathematics (section Graph theory)
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...
26 KB (2,768 words) - 13:50, 31 July 2024
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...
12 KB (959 words) - 07:51, 18 July 2024
Degree matrix (category 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...
3 KB (375 words) - 03:40, 21 September 2023
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a...
38 KB (4,839 words) - 07:44, 16 July 2024
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...
11 KB (1,450 words) - 17:21, 31 July 2024
Cycle space (category Algebraic graph theory)
can also be described in terms from algebraic topology as the first homology group of the graph. Using homology theory, the binary cycle space may be generalized...
18 KB (2,511 words) - 12:40, 14 June 2024
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...
3 KB (358 words) - 14:43, 28 May 2024
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...
16 KB (1,936 words) - 02:36, 7 August 2024
Representation (mathematics) (section Graph theory)
6950, doi:10.4153/cjm-1966-014-3, MR 0186575 Biggs, Norman (1994), Algebraic Graph Theory, Cambridge Mathematical Library, Cambridge University Press,...
11 KB (1,209 words) - 11:19, 9 January 2024
Dragan Marušič (category Graph theorists)
of Koper. His research focuses on topics in algebraic graph theory, particularly the symmetry of graphs and the action of finite groups on combinatorial...
10 KB (1,037 words) - 08:30, 13 February 2024