Q: Prove that for every n≥5 there exists a graph with n vertices, all of which have degree 4 Given n, describe formally, for $1\le$$\\ i\le$ n, the ith row in the adjacency matrix, such that it includes exactly 4 ones and n-4 zeros (use 'mod' in your formal description, to make it simple and uniform for all $1\le$$\\ i\le$ n . Prove that for every $1\le$$\\ i\le$ n the ith column includes exactly 4 ones and n-4 zeros. 
My attempt:
Say we have a graph of 7 vertices, all numbered by the proper row/column. as we place an edge by (i+1)mod n and (i+2)mod n.
As the matrix is asymmetrical we know it hold as an undirected graph. Thus, there exist a graph with n vertices accordingly
I would appreciate further guidance and if the direction is wrong, a way to prove this.

A: Place the $n\ge 5$ vertices in a circle. If every vertex is connected with the two left and the two right neighbours, we get the desired graph.
