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2. Turn-by-turn navigation - Wikipedia

   en.wikipedia.org/wiki/Turn-by-turn_navigation

   Turn-by-turn systems typically use an electronic voice to inform the user whether to turn left or right, the street name, and the distance to the next turn. [ 3 ] Mathematically, turn by turn navigation is based on the shortest path problem within graph theory , which examines how to identify the path that best meets some criteria (shortest ...

3. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   A drawing of a graph. 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 (also called arcs, links or lines ).

4. Tournament (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tournament_(graph_theory)

   Tournament (graph theory) In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently, a tournament is an orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in ...

5. Seven Bridges of Königsberg - Wikipedia

   en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

   Seven Bridges of Königsberg. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 [ 1] laid the foundations of graph theory and prefigured the idea of topology. [ 2]

6. Turán's theorem - Wikipedia

   en.wikipedia.org/wiki/Turán's_theorem

   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 ...

7. Orientation (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Orientation_(graph_theory)

   Among directed graphs, the oriented graphs are the ones that have no 2-cycles (that is at most one of (x, y) and (y, x) may be arrows of the graph). [ 1] A tournament is an orientation of a complete graph. A polytree is an orientation of an undirected tree. [ 2] Sumner's conjecture states that every tournament with 2n – 2 vertices contains ...

8. Connectivity (graph theory) - Wikipedia

   en.wikipedia.org/wiki/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 isolated subgraphs. [1] It is closely related to the theory of network flow problems.

9. Algebraic graph theory - Wikipedia

   en.wikipedia.org/wiki/Algebraic_graph_theory

   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, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants .