   # Use the greedy algorithm to find a Hamiltonian circuit starting at vertex A in the weighted ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 12ES
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.

### Explanation of Solution

Given information:

Given, weighted graph is:

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 18, 16, 9, 17, 14

Hence, as per the Greedy Algorithm the edge with weight 9 is selected i.e. path reaches D.

Vertex D is of degree 5 and the weights of the connected edges are 25, 21, 9, 6, 12

Hence, as per the Greedy Algorithm the edge with weight 6 is selected i.e. path reaches F.

Vertex F is of degree 5 and the weights of the connected edges are 14, 16, 4, 6, 26

Hence, as per the Greedy Algorithm the edge with weight 4 is selected i.e. path reaches C.

Vertex C is of degree 5 and the weights of the connected edges are 5, 16, 4, 20, 25

The least of the weights is 4 but it leads to vertex F which is already visited...

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