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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 15ES

Textbook Problem

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Use the edge-picking algorithm to find a Hamiltonian circuit in the indicated graph.

Graph in Exercise 11

To determine

To determine a Hamiltonian circuit in the weighted graph using the edge-picking 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 edge-picking algorithm states to mark the edge that has the smallest weight in the complete graph. Then, the edge with the next smallest weight is marked as long as it does not complete a circuit and does not add a third marked edge to a single vertex. This process continues till no longer an edge can be marked. Then the final edge completing the Hamiltonian circuit is marked.

Here, the least weight in the graph is 1.

Hence, the edge AD having the weight 1 is marked first.

The next least weight in the graph is 2.

Hence, the edges AC and BD having the weight 2 are marked.

The next least weight in the graph is 3.

Here, the edges CD and BC have weight 3. But marking CD add a third side (at D) and marking BC would complete the circuit...

Mathematical Excursions (MindTap Course List)

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