Objective

This experiment aims to help students understand and practice key concepts in graph theory through interactive tasks. Students will learn to:

• Identify and construct Hamiltonian cycles in graphs
• Determine whether a graph is Eulerian
• Solve the Traveling Salesman Problem using weighted graphs

Task 1: Drawing Hamiltonian Cycle

1. Draw a Hamiltonian cycle by following these steps:

   • Click edges to form a closed loop
   • Start and end at the same node
   • Visit each node exactly once

2. Submit your solution:

   • If a Hamiltonian cycle exists: Select edges in the correct order, then click submit
   • If no Hamiltonian cycle exists: Click submit without selecting any edges

3. Review your answer:

   • Check the answer in the observation window
   • Read the provided explanation

4. Try another graph:

   • Click the "change graph" button to get a new graph

Task 2: Validating Eulerian Graphs

1. Analyze the given graph:

   • Use the buttons in the Observation window
   • Determine if the graph is Eulerian

2. Verify your answer:

   • Check your response in the observation window

3. Practice with different graphs:

   • Click the "change graph" button to get a new graph

Task 3: Finding Shortest Weighted Routes

1. Analyze the weighted graph:

   • Find the shortest route that:
     • Visits all nodes exactly once
     • Returns to the starting node

2. Draw your solution:

   • Select edges in order to show the shortest weighted path

3. Check your work:

   • Verify your answer in the observation window

4. Try more examples:

   • Click the "change graph" button to get a new graph