Construction of eleven and thirteen mutually orthogonal path-squares

Document Type : Original Article

Author

Dept. of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufya University, EGYPT

Abstract

In this paper, we give an introduction to an area of combinatorial theory which deals with. mutually orthogonal  (MOGSs) where  is a spanning subgraph of  That is, we will investigate the maximal number of a collection of  of order n  which are orthogonal in pairs. The most general object studied in this theory is a set of the so-called mutually orthogonal Latin squares (MOLSs) of order  which are equivalent to mutually orthogonal if . That is, this approach is an extension of MOLSs. Our objective in this paper is to discuss two direct constructions from conjecture in [7] for all prime numbers   to obtain MOGSs  where .

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References

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