Vertex cover problem

Implement ILP for the vertex cover problem using Gurobi. Your program should ask the user the number of vertices (say X) of the graph. Then you have to randomly generate a connected graph that will have X vertices.
You have to randomly assign edges in such a way so that the range of edges for any vertex should be between 1 to X/2. Again, you have to make sure that your graph is connected. If your graph is not connected then you will not get any marks for this question.
Once, your graph is ready then solve ILP to get the solution of the problem

Given a 7x7 game board (see the following table), mark the grids to ensure no more than one grid in the same row or the same column are marked. Also, try to maximize the sum of the values in those marked grids.

5    4    6    7    1    5    6
                        
9    8    5    1    1    2    3
                        
1    7    4    6    2    3    5
                        
1    1    2    4    2    6    2
                        
15    12    1    3    10    8    2
                        
16    17    1    1    6    6    2
                        
3    5    8    1    2    1    1
                        
The game board (indicates the value of each grid) data is shown as follows, you can directly copy it to your code.

P = [

[5,4,6,7,1,5,6],

[9,8,5,1,1,2,3],

[1,7,4,6,2,3,5],

[1,1,2,4,2,6,2],

[15,12,1,3,10,8,2],

[16,17,1,1,6,6,2],

[3,5,8,1,2,1,1]

]