a. Refer to the Graph 3.1 below. The vertices represent houses. An edge connects two houses...

   

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a. Refer to the Graph 3.1 below. The vertices represent houses. An edge connects two houses if there is a communication link between the two. Notice that any house can communicate with any other either directly through a communication link or by having others relay message. i. ii. 8 5 7 10 6 Graph 3.1 Show, by giving example, that communication among all houses is still possible even if some communication links are broken. What is the maximum number of communication links that can be broken with communication among all houses still possible? b. Explain what Hamiltonian cycle is and what Euler cycle is. Provide an example of a graph that has a Hamiltonian cycle and an Euler cycle. Prove that the graph has the specified properties. How does you apply this in a real-world situation? a. Refer to the Graph 3.1 below. The vertices represent houses. An edge connects two houses if there is a communication link between the two. Notice that any house can communicate with any other either directly through a communication link or by having others relay message. i. ii. 8 5 7 10 6 Graph 3.1 Show, by giving example, that communication among all houses is still possible even if some communication links are broken. What is the maximum number of communication links that can be broken with communication among all houses still possible? b. Explain what Hamiltonian cycle is and what Euler cycle is. Provide an example of a graph that has a Hamiltonian cycle and an Euler cycle. Prove that the graph has the specified properties. How does you apply this in a real-world situation?