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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 .
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.
The Mathematical Bridge is a wooden footbridge in the southwest of central Cambridge, England. It bridges the River Cam about one hundred feet northwest of Silver Street Bridge and connects two parts of Queens' College. Its official name is simply the Wooden Bridge [2] or Queens' Bridge. [3] It is a Grade II listed building. [1]
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Then the bridge number of a knot can be found as the minimum number of bridges required for any diagram of the knot. [1] Bridge numbers were first studied in the 1950s by Horst Schubert. [2] [3] The bridge number can equivalently be defined geometrically instead of topologically. In bridge representation, a knot lies entirely in the plane apart ...
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