Problem 71 I use Fleury's Algorithm to dete... [FREE SOLUTION]

Chapter 14: Problem 71

I use Fleury's Algorithm to determine if a graph contains Euler paths or Euler circuits.

Short Answer

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The application of Fleury's Algorithm entails recognizing the number of odd degree vertices, ensuring the graph's connectedness excluding 0 degree vertices, and applying the algorithm by removing traversed edges until all edges are traversed. The presence of Euler circuit or path is dictated by the number of odd degree vertices in the graph; If all vertices are of even degree, the circuit exists; If the number of odd degree vertices is 2, the path exists; In other cases, neither an Euler path or circuit exists.

Step by step solution

Identify Odd and Even Vertices

Apply the degree rule to the graph. The degree rule states that an Eulerian circuit is existent if all vertices in the graph have an even degree. An Eulerian path exists only when exactly zero or two vertices have an odd degree, while the rest are even. The path starts at one of the odd degree vertices if there are any odd vertices.

Check for Connectedness

Verify if the graph is connected. A graph is connected if there is a path from any vertex to any other vertex. We don't consider vertices of degree 0 when checking for connectivity. Use either Depth-First Search or Breadth-First Search to check for connectedness.

Apply Fleury's Algorithm

If the graph is connected and adheres to the odd number rule, proceed with Fleury's Algorithm. Choose the starting vertex (any vertex if every vertex has even degree, or the odd degree vertex if it exists) and follow edges one at a time. If the edge followed is a bridge (an edge whose removal disconnects the graph), make sure there are no other available edges. After the edge is traversed, remove it from the graph. Continue the process until all the edges have been traversed. You've created an Euler path or circuit.

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91影视

I use Fleury's Algorithm to determine if a graph contains Euler paths or Euler circuits.

Short Answer

Step by step solution

Identify Odd and Even Vertices

Check for Connectedness

Apply Fleury's Algorithm

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