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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 11ES

Textbook Problem

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Use the greedy algorithm to find a Hamiltonian circuit starting at vertex A in the weighted

To determine

To determine a Hamiltonian circuit starting at vertex A in the weighted graph using the greedy algorithm.

**Given information:**

Given, weighted graph is:

â€ƒâ€ƒ

**Calculation:**

A path in a Hamiltonian graph is said to be a Hamiltonian Circuit if it begins and ends at the same vertex and passes through each vertex of a graph exactly once.

The greedy algorithm states to travel along a connected edge that has the smallest weight that is not yet visited. This process continues till all the vertices are visited and returned to the starting vertex.

Here, the vertex A is selected.

Vertex A is of degree 5 and the weights of the connected edges are 8, 5, 1, 2, 7

Hence, as per the Greedy Algorithm the edge with weight 1 is selected i.e. path reaches D.

Vertex D is of degree 5 and the weights of the connected edges are 9, 7, 1, 2, 3.

The least of the weights is 1 but it leads to vertex A which is already visited.

Hence, as per the Greedy Algorithm the edge with weight 2 is selected i.e. path reaches B.

Vertex B is of degree 5 and the weights of the connected edges are 7, 4, 9, 2, 3

The least of the weights is 2 but it leads to vertex D which is already visited...

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