1Department of Mathematics, K. N. Toosi University of Technology
2K. N. Toosi university of Technology University, Tehran-Iran.
In this paper, the type-II matrices on (negative) Latin square graphs are considered and it is proved that, under certain conditions, the Nomura algebras of such type-II matrices are trivial. In addition, we construct type-II matrices on doubly regular tournaments and show that the Nomura algebras of such matrices are also trivial.