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y. =. x. 3. to save your graphs! Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
These notes include major de nitions, theorems, and proofs for the graph theory course given by Prof. Maria Axenovich at KIT during the winter term 2019/20. Most of the content is based on the book \Graph Theory" by Reinhard Diestel [4]. A free version of the book is available at http://diestel-graph-theory.com. Conventions:
12 Ιουλ 2021 · Let the graph \(G\) be defined by \(V = \{w, x, y, z\}\) and \(E = \{e_1, e_2\}\), where \(e_1 = \{w, x\}\) and \(e_2 = \{w, y\}\). There are no loops or multiple edges, so \(G\) is a simple graph. The edge \(e_2\) has endvertices \(w\) and \(y\).
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A graph with no loops and no multiple edges is a simple graph. A graph with no loops, but possibly with multiple edges is a multigraph. The condensation of a multigraph is the simple graph formed by eliminating multiple edges, that is, removing all but one of the edges with the same endpoints.
Graph Theory is a relatively new area of mathematics, first studied by the super famous mathematician Leonhard Euler in 1735. Since then it has blossomed in to a powerful tool used in nearly every branch of science and is currently an active area of mathematics research.
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