... qd2+k−1 qk−1. From (2.6) and (2.8), the number of copies of Kkin E is(1 + o(1))|E|kk!q−(k2)..This implies that the number of the number of k-tuples of k mutually orthogonalvectors ... Jnq,dis the all one matrix and Inq,dis the identity matrix, both of size nq,d×nq,d). Therefore, the largest eigenvalue of V is Dq,dand the absolute values of all other eigenvalues are either(q ... where two vectors are equivalent if one is a multiple of the other by an element of the field. Let GP(q, d) denote the graph whose vertices are the points of P G(q, d) and two(not necessarily...