Recursive approach for constructing power graph squares

Mutually orthogonal Latin squares are very important combinatorial designs for a wide range of applications such as wireless sensor networks, cryptography, experimental designs, and many others. Computing the maximum number of mutually orthogonal Latin squares of order n is known as a computationally hard problem in combinatorics. Here, we present the concept of mutually orthogonal graph squares as general and graph forms of orthogonal Latin squares. We present an approach for constructing a graph square and recursive construction of mutually orthogonal graph squares. The accuracy of the presented approach is proved. Moreover, this approach is shown to be systematic for computing the maximum number of mutually orthogonal graph squares for a power graph.