52 Removal Edge 5 Points Let G Graph E Edge G Denote G E Graph Obtained G Removal Fo E Ver Q43854848
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5.2 Removal of an edge (5 points) Let G be a graph and e be an edge of G. We denote by Ge the graph obtained from G by removal fo e. That is, the vertices of Ge 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 such that that are adjacent in G. The program should print the adjacency matrix of G{ij} (that is G with the edge between i and 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 Gif 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 false 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 5 Processing the list of edges 5.1 Listing all the edges (5 points) Write an O(na) 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 05 1 5 Show transcribed image text 5.2 Removal of an edge (5 points) Let G be a graph and e be an edge of G. We denote by Ge the graph obtained from G by removal fo e. That is, the vertices of Ge 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 such that that are adjacent in G. The program should print the adjacency matrix of G{ij} (that is G with the edge between i and 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 Gif 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 false 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
5 Processing the list of edges 5.1 Listing all the edges (5 points) Write an O(na) 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 05 1 5
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Answer to 5.2 Removal of an edge (5 points) Let G be a graph and e be an edge of G. We denote by Ge the graph obtained from G by …
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