Graph Tour Algorithm

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What is a Euler or Eulerian tour?

https://iq.opengenus.org/what-is-a-euler-or-eulerian-tour/

An Euler tour or Eulerian tour in an undirected graph is a tour/ path that traverses each edge of the graph exactly once. Graphs that have an Euler tour are called Eulerian graphs. Necessary and sufficient conditions. An undirected graph has a closed Euler tour if and only if it is connected and each vertex has an even degree.Author: Alexa Ryder

8.11. The Knight’s Tour Problem — Problem Solving with ...

https://runestone.academy/runestone/books/published/pythonds/Graphs/TheKnightsTourProblem.html

The Knight’s Tour Problem¶ Another classic problem that we can use to illustrate a second common graph algorithm is called the “knight’s tour.” The knight’s tour puzzle is played on a chess board with a single chess piece, the knight.

Travelling salesman problem - Wikipedia

https://en.wikipedia.org/wiki/Travelling_salesman_problem

This leaves us with a graph where every vertex is of even order which is thus Eulerian. Adapting the above method gives the algorithm of Christofides and Serdyukov. Find a minimum spanning tree for the problem; Create a matching for the problem with the set of cities of odd order. Find an Eulerian tour for this graph; Convert to TSP using ...

Graph Data Structure And Algorithms - GeeksforGeeks

https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/

In the above Graph, the set of vertices V = {0,1,2,3,4} and the set of edges E = {01, 12, 23, 34, 04, 14, 13}. Graphs are used to solve many real-life problems. Graphs are used to represent networks. The networks may include paths in a city or telephone network or circuit network. Graphs are also used in social networks like linkedIn, Facebook.

Fleury's Algorithm for printing Eulerian Path or Circuit ...

https://www.geeksforgeeks.org/fleurys-algorithm-for-printing-eulerian-path/

Nov 25, 2019 · There are no more edges left, so we stop here. Final tour is ‘2-0 0-1 1-2 2-3’. See this for and this fore more examples.. Following is C++ implementation of above algorithm. In the following code, it is assumed that the given graph has an Eulerian trail or Circuit.

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