Computer Science Application of Graph Algorithms.

There are N cities and the cost of providing direct flight between any two cities is given. Determine a set of direct flights to offer so that all cities are connected but also to minimize the total cost of providing all these direct flights. You may ignore the direction of flights and assume that the direct flight between any two selected cities is bi-directional.

1) Give clear explanations on how this problem can be solved using graph model: What are the vertices representing? What are the edges representing?

2) Describe the algorithm used to find the answer.

3) Analyze the time complexity of your algorithm.