Dear participants of the project,

we start to present the current results in graph form. As we already wrote, the scientific goal of the project is to reveal subsets structures of orthogonal diagonal Latin squares of rank 9. A good form to represent such subsets is a graph. Each its vertice is a single square, and an edge between two vertices means that these two squares are orthogonal. The considered graphs are of great interest when one studies ODLSs with fundamental or applied goals.

With help of the RakeSearch algorithm, we discover separate vertices of such graphs. The RakeSearch algorithm implies that not every possible pair of ODLSs can be found, but only those that can be obtained by rows permutations. Such squares are being "hooked" like jewels among the withered grass. And then, using post-processing, we restore the whole graph.

So far, we have discovered 18 types of such graphs. The first one is the "Necklace". There are multiple instances of each graph type. The most common type is the simple pair. Our special thanks go to Stepan Kochemazov and Eduard Vatutin (evatutin) for their ideas and work used for implementing post-processing programs! Visualization was implemented with Gephi software.

We hope that graph form of results will be interesting to you!
Good luck and happy crunching!