Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques

Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments designing an experiment permit effective statistical analysis results, they encode incidence structure finite geometries, encapsulate groups and more general algebraic objects known as quasigroups, produce optimal density error-correcting codes. This paper gives some new results on graph squares. Mutually generalize interestingly. are area combinatorial design theory that has many applications optical communications, wireless cryptography, storage system design, algorithm analysis, communication protocols, mention just a few areas. In this paper, novel product techniques considered. Proposed half-starters’ vectors Cartesian product, function tensor graphs. It is shown by taking subgraphs complete bipartite graphs, one can obtain enough larger Also, we try find minimum number for certain graphs based proposed techniques. As direct application techniques, disjoint unions stars constructed. All constructed be used generate graph-orthogonal arrays authentication