On mutually orthogonal certain graph squares

This paper gives some new results on mutually orthogonal graph squares (MOGS). These generalize mutually orthogonal Latin squares in an interesting way. As such, the topic is quite nice and should have broad appeal. MOGS have strong connections to core fields of finite algebra, cryptography, finite geometry, and design of experiments. We are concerned with the Kronecker product of mutually orthogonal graph squares to get new results of the mutually orthogonal certain graphs squares.