# Thread: Adjacency Matrix

1. ## Adjacency Matrix

Hi all;
I need the proof of the folowing Theorem:
If X is the adjacency matrix of a graph G with n vertices, and
$Y=X+X^2+X^3+....+X^{n-1}$, then G is disconnected if and only if there exist at least one entry in matrix Y that is zero.
Best Wishes

2. What ideas have you had so far?