Edges and graphs

The solution below got cut off. Please let me know what is the total solution: problem: The number of strongly connected components in a graph G is k. By how much can this number change if we add a new edge? solution: If we add an edge to a biconnected graph with k strongly connected components, then there are three scenarios: the endpoints of the edge lie in different strongly connected component and there is no path between the two in the original graph, the endpoints of the edge lie in different strongly connected component and there is a path between the two in the original graph, and the endpoints of the edge lie in the same strongly connected component. In the ... click for more

Flow network

(See attached file for full problem description)

Edge connectivity

The edge connectivity of an undirected graph is the minimum number k of edges that must be removed to disconnect the graph. For example, the edge connectivity of a tree is 1, and the edge connectivity of a cyclic chain of vertices is 2. Show how the edge connectivity of an undirected graph G = (V, E) can be determined by running a maximum-flow algorithm on at most |V| flow networks, each having O(V) vertices and O(E) edges.

Maximum cardinality matching algorithm

A tree is a connected undirected graph with no cycles. Design a linear time algorithm to find a maximum cardinality matching in a tree.

Compare the two non-sequential file structure models

Compare the two non-sequential file structure models: the random (hashed) file and the index file. What advantages does the first one have over the second and what advantages does the second have over the first? What would be your criteria for choosing one over the other for different applications?