5 Processing the list of edges 5.1 Listing all the edges (5 points) Write an O(n 2 ) program whose input is the adjacency matrix of a graph G. The program should print the list of all the edges (without repetition). For example, if the vertices of the graph are 0, 1, 2, 3, 4, 5 with 0 adjacent to 1 and 5, 1 adjacent to 5 2 adjacent to 3 and 4 and 3 adjacent to 4 then the printed list should be something like. 0 1 0 5 1 5 2 3 2 4 3 4 5.2 Removal of an edge (5 points) Let G be a graph and e be an edge of G. We denote by G\e the graph obtained from G by removal fo e. That is, the vertices of G \ e are the same as in G and the edges of G \ e are all the edges of G but e. Write a program whose input is the adjacency matrix of a graph G and two vertices i and j such that that are adjacent in G. The program should print the adjacency matrix of G \ {i, j} (that is G with the edge between i and j being removed). 5.3 Listing all the bridges (10 points) Let G be a connected graph and e be an edge of G. We say that e is a bridge of G if G \ e is not connected (put it differently, the removal of e breaks the connectivity of G). Assume that we have a function Connect whose input is the adjacency matrix of a graph and the output is true if the graph is connected and f alse otherwise. Using this procedure, design an algorithm that prints all the bridges of G. Hint: Use the algorithm for the first part of that question for exploration of all the edges. Rather than printing the curretly considered edge straightaway, use the Connect procedure to check whether the given edges is a bridge (the whole non-triviality of this task is how to apply Connect in this context). Print only those edges for which Connect retrns true.

java or python

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