1. Describe how a cycle is similar to a Euler circuit. 2. Write a set of step-by-step instructions to form an algorithm for converting an inefficient network into an efficient network. 3. The numbers in the following graphs depict the cost associated with building a railroad between cities represented by vertices. For each graph, test your algorithm. Does it yield the most efficient network? If not, try modifying your algorithm. 5 5 Network I Network II 4. Use Kruskal's Algorithm to find a minimal spanning tree in the following graph. 8 5 10 12 1 5. Do all graphs have spanning trees? Are spanning trees unique? 10 10