Adjacency Matrix(Graph) - Insertion & DeletionGiven an adjacency matrix g[][] of a graph consisting of N vertices, the task is to modify the matrix after insertion of all edges[] and removal of edge between vertices (X, Y). In an adjacency matrix, if an edge exists between vertices i and j of the graph, then g[i][j] = 1 and g[j][i] = 1. If no edge exists between these two vertices, then g[i][j] = 0 and g[j][i] = 0.Input: N = 6, Edges[] = {{0, 1}, {0, 2}, {0, 3}, {0, 4}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {3, 5}}, X = 2, Y = 3

To solve this problem, you can follow these steps:

1. Initialize an N x N matrix with all elements as 0. This will represent the adjacency matrix of the graph.

2. For each edge in the Edges array, set the corresponding elements in the adjacency matrix to 1. For example, if there is an edge between vertices i and j, set g[i][j] = 1 and g[j][i] = 1.

3. After all edges have been inserted, remove the edge between vertices X and Y by setting g[X][Y] = 0 and g[Y][X] = 0.

Here is a Python code snippet that implements these steps:

def modify_matrix(N, Edges, X, Y):
    # Step 1: Initialize the adjacency matrix
    g = [[0 for _ in range(N)] for _ in range(N)]
    
    # Step 2: Insert all edges
    for edge in Edges:
        i, j = edge
        g[i][j] = 1
        g[j][i] = 1
    
    # Step 3: Remove the edge between X and Y
    g[X][Y] = 0
    g[Y][X] = 0
    
    return g

You can call this function with your inputs to get the modified adjacency matrix:

N = 6
Edges = [(0, 1), (0, 2), (0, 3), (0, 4), (1, 3), (2, 3), (2, 4), (2, 5), (3, 5)]
X = 2
Y = 3

print(modify_matrix(N, Edges, X, Y))

This will print the adjacency matrix after all insertions and the deletion.