# Euler circuits

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Write ideas for a one-page summary on each of the following three topics from your text:

1. Euler circuits, including their definition, recognition, how to create them, and how to prove they exist.

Describe Nearest Neighbor, Sorted Edges, and Kruskal's algorithms. Illustrate their use.

Describe the characteristics of Simplex Method and Alternative to the Simplex Method. Illustrate their use in solving a practical problem.

2. Find three Web sites that demonstrate a practical application of the use of Euler circuits. Write a five to six sentence description of each Web site. For more information on a Links Assignment and samples, please go here: Links Assignment

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The solution assists with writing ideas for a summary on each of the given topics regarding Euler circuits.

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Euler Circuit is a special circuit that passes along each edge exactly once. There is a theorem, the Euler theorem that allows one to know exactly when it is possible to find an Euler circuit on a graph. Nearest neighbor is when you pick a starting vertex and form a circuit which starts and ends at that vertex by always travelling along the edge coming out of your vertex that has the lowest weight, being careful to never visit a vertex twice until all have been visited once. This is a quick and easy method, even though it may not give the best possible answer. Sorted edges occur when you "grab" edges until you have a complete circuit. The edge grabbed will always be the one with the lowest weight that has not been grabbed yet, as long as grabbing it does not cause a circuit to form ...

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