Eulerian circuit
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Eulerian circuit
A graph is a collection of vertices, or nodes, and edges between some or all of the vertices. When there exists a path that traverses each edge exactly once such that the path begins and ends at the same vertex, the path is known as an Eulerian circuit and the graph is known as an Eulerian graph. Eulerian refers to the Swiss mathematician Leonhard Euler, who invented graph theory in the 18th century.
An Eulerian circuit is a path in a graph that traverses each edge exactly once and begins and ends at the same vertex. This concept originated from the Königsberg bridge problem, where the question was whether it was possible to cross all seven bridges of the city exactly once. Swiss mathematician Leonhard Euler proved in 1735 that such a walk was impossible, establishing the foundation for graph theory. A graph has an Eulerian circuit if it is connected and all its vertices have an even degree.12
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