Search for "Graph theory" in article titles:

1. Graph theory: A branch of discrete mathematics, distinguished by its geometric approach to the study of various objects. The principal object of the theory is a graph and its generalizations. (Mathematics) [100%] 2023-11-06 [Graph theory]
2. Graph theory: In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges ... (Area of discrete mathematics) [100%] 2023-12-19 [Graph theory]
3. Graph theory: Graph theory is the field of mathematics which deals with the study of graphs. A graph is defined as a set of vertices or nodes and edges or arcs which join the nodes. [100%] 2023-07-05
4. Graph theory: In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges ... (Area of discrete mathematics) [100%] 2024-08-24 [Graph theory]
5. Periodic graph (graph theory): In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that F(G) is isomorphic to G. For example, every graph ... (Graph theory) [86%] 2023-12-14 [Graph invariants] [Graph operations]...
6. Loop (graph theory): In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. (Graph theory) [81%] 2023-11-28 [Graph theory]
7. Haven (graph theory): In graph theory, a haven is a certain type of function on sets of vertices in an undirected graph. If a haven exists, it can be used by an evader to win a pursuit–evasion game on the graph, by ... (Graph theory) [81%] 2023-11-19 [Graph theory objects] [Graph minor theory]...
8. Girth (graph theory): In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be ... (Graph theory) [81%] 2023-12-13 [Graph invariants]
9. Split (graph theory): In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. (Graph theory) [81%] 2023-10-17 [Graph theory objects]
10. Saturation (graph theory): Given a graph \displaystyle{ H }[/math], another graph \displaystyle{ G }[/math] is \displaystyle{ H }[/math]-saturated if \displaystyle{ G }[/math] does not contain a (not necessarily induced) copy of \displaystyle{ H }[/math], but adding any edge to \displaystyle{ G }[/math ... (Graph theory) [81%] 2023-11-30 [Matching (graph theory)]
11. Star (graph theory): In graph theory, a star Sk is the complete bipartite graph K1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define Sk to be ... (Graph theory) [81%] 2023-11-30 [Trees (graph theory)] [Parametric families of graphs]...
12. Interval (graph theory): In graph theory, an interval I(h) in a directed graph is a maximal, single entry subgraph in which h is the only entry to I(h) and all closed paths in I(h) contain h. Intervals were described in ... (Graph theory) [81%] 2023-11-05 [Graph theory objects] [Control-flow analysis]...
13. Dimension (graph theory): In mathematics, and particularly in graph theory, the dimension of a graph is the least integer n such that there exists a "classical representation" of the graph in the Euclidean space of dimension n with all the edges having unit ... (Graph theory) [81%] 2023-10-23 [Geometric graph theory] [Graph invariants]...
14. Tree (graph theory): In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected ... (Graph theory) [81%] 2023-11-10 [Trees (graph theory)]
15. Book (graph theory): In graph theory, a book graph (often written \displaystyle{ B_p }[/math] ) may be any of several kinds of graph formed by multiple cycles sharing an edge. One kind, which may be called a quadrilateral book, consists of p quadrilaterals sharing ... (Graph theory) [81%] 2023-11-04 [Parametric families of graphs] [Planar graphs]...
16. Cut (graph theory): 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 endpoint in each subset of the partition. (Graph theory) [81%] 2023-11-30 [Graph connectivity] [Combinatorial optimization]...
17. Boundary (graph theory): In graph theory, the outer boundary of a subgraph H of a graph G is the set of vertices of G not in H that have a common edge with a vertex in H. Its inner boundary is the set ... (Graph theory) [81%] 2023-11-28 [Graph theory]
18. Spectral graph theory: In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix ... (Linear algebra aspects of graph theory) [81%] 2024-01-12 [Algebraic graph theory] [Spectral theory]...
19. Loop (graph theory): In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. (Graph theory) [81%] 2023-11-29 [Graph theory]
20. Extremal graph theory: Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. [81%] 2023-09-18 [Extremal graph theory]
21. Distance (graph theory): In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or ... (Graph theory) [81%] 2023-11-01 [Graph theory] [Metric geometry]...
22. Bridge (graph theory): In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. Equivalently, an edge is a bridge if and only if it is not ... (Graph theory) [81%] 2023-08-30 [Graph connectivity]
23. Map (graph theory): In topology and graph theory, a map is a subdivision of a surface such as the Euclidean plane into interior-disjoint regions, formed by embedding a graph onto the surface and forming connected components (faces) of the complement of the ... (Graph theory) [81%] 2023-11-30 [Topology] [Graph theory objects]...
24. Path (graph theory): In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A ... (Graph theory) [81%] 2023-11-15 [Graph theory objects] [Graph connectivity]...
25. Connectivity (graph theory): In 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 to be removed to separate the remaining nodes into two or more ... (Graph theory) [81%] 2023-12-30 [Graph connectivity]
26. Spectral Graph Theory: This page, as of now, contains resources to learn spectral graph theory. [81%] 2024-01-12 [Graph theory]
27. Thickness (graph theory): In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists a collection of k planar graphs, all having the same ... (Graph theory) [81%] 2023-11-28 [Graph invariants] [Planar graphs]...
28. Connectivity (graph theory): In 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 to be removed to separate the remaining nodes into two or more ... (Graph theory) [81%] 2023-11-28 [Graph connectivity]
29. Geometric graph theory: Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs ... (Subfield of graph theory) [81%] 2023-09-10 [Geometric graph theory]
30. Evolutionary graph theory: Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. (Approach to studying how topology affects evolution of a population) [81%] 2024-01-12 [Evolution] [Application-specific graphs]...