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A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. 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. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. 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]
A connected graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs. [2]
A time–distance diagram is a chart with two axes: one for time, the other for location. The units on either axis depend on the type of project: time can be expressed in minutes (for overnight construction of railroad modification projects such as the installation of switches) or years (for large construction projects); the location can be (kilo)meters, or other distinct units (such as ...
This is a list of major infrastructure on the Northeast Corridor, a rail line running through the Northeastern United States.The list includes major interlockings, bridges, tunnels, and past and present stations, including the Massachusetts Bay Transportation Authority's Orange Line, the Washington Metro's Orange Line, and PATH stations on separate tracks but sharing the right-of-way.
7 lanes of roadway and trains: Double-decker bridge with 5 westbound lanes and 2 eastbound lanes. 3 of the westbound lanes and the subway are below the other 4 lanes. Williamsburg Bridge: 1903: 7,308.0 2,227.48: 8 lanes of roadway (4 in each direction) and trains: J train on the Williamsburg Bridge: Queensboro Bridge: 1909: 3,724 1,135
A graph with 6 vertices and 7 edges. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Cable-stayed bridge and Suspension bridge: 1,408 m (4,619 ft) Yavuz Sultan Selim Bridge, [2] Istanbul: Cantilever bridge: 549 m (Quebec bridge) 1042.6 m (Forth Bridge) Cantilever spar cable-stayed bridge: Clapper bridge: Covered bridge: Girder bridge: Continuous span girder bridge Integral bridge: Extradosed bridge: 1,920 m Arrah–Chhapra ...