- Find a connected graph of n vertices for which each of the powers AG^1 , AG^2 , . . . of the adjacency matrix contains some zero elements.
for this I drew two vertices and linked them together with one edge, then I built the adjacency matrix with rows (0 1) and (1 0). I showed that for n>1, AG^n is the identity matrix thus containing some zero elements. I just have not proved this for n vertices, I'm just at two. Can I take a step further and say that any n vertices connected in a straight line satisfy the conditions ?