we have a simple graph that it's vertices are {v_1, v_2, ... v_n}.

The Adjacency matrix of this graph is A= (a_ij) so that;

(a_ij)=1 if i+j belongs to the Fibonacci sequence. (a_ij)=0 if i+j doesn't belong to the Fibonacci sequence.

We claim that the determinant of this matrix when n is odd is 0 and when n is even is 1 or -1 or 0. How can we prove this claim?