Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. C++ v Algorithm Connected (A[0..n-1, 0..n-1]) { //Input: Adjacency matrix A of an undirected graph G //Output: 1 (true) if G is connected and 0 (false) if it is not if n == 1 return 1; // //one-vertex graph is connected by definition else { } if not Connected (A[0..n-2, 0..n-2]) return 0; else { for j = 0 to n - 2 do { if A[n-1, j] return 1; } return 0; Co ption ... Does this algorithm work correctly for every undirected graph with n vertices? If you answer YES, indicate the algorithm's efficiency class in the worst case. If you answer NO, provide a counter example.

5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…

Weighted Graph Applications Demonstration Java Data Structures. Figure 29.23 illustrates a weighted graph with 6 vertices and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). You can therefore attach proper content files with dot txt, png, jpg or jpeg extensions  Be sure the final trees or path lists are clearly visible in your solution.  You don't need to show the solution development or progress, just the result.

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