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Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Learn about different types of graphs, their properties, problems and applications in various fields of mathematics, physics, chemistry and biology.
A graph is a structure consisting of vertices and edges, where edges can be directed or undirected. Learn the definitions, properties, examples and applications of graphs and related concepts in graph theory.
Learn about the problem of finding a path between two vertices in a graph with minimum weight or length. Compare different algorithms and their time complexities for various types of graphs and weights.
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...
Geometric graph theory is a subfield of graph theory that studies graphs defined by geometric means, such as planar, triangulation, Euclidean, intersection, and partial cube graphs. Learn about the different types of geometric graphs, their properties, and their applications in network science.
There are two definitions. In the most common one, the disjoint union of graphs, the union is assumed to be disjoint. Less commonly (though more consistent with the general definition of union in mathematics) the union of two graphs is defined as the graph (V 1 ∪ V 2, E 1 ∪ E 2). graph intersection: G 1 ∩ G 2 = (V 1 ∩ V 2, E 1 ∩ E 2); [1]
Learn about the mathematical definition, types, and properties of knots, which are embeddings of the circle in three-dimensional space. Explore the history, applications, and challenges of knot theory, a branch of topology that studies knots and their complements.
Learn about the history, devices and services of turn-by-turn navigation, a feature of some satellite navigation devices that provides spoken or visual directions. Find out which apps and websites offer turn-by-turn navigation, including Google Maps, HERE WeGo, Waze and more.