Geodesic
Orthogonality graphs of direct sums of rings and semisimple Artinian rings
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 138-166

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The paper studies the orthogonality relation graphs for noncommutative rings. Known results on the diameters of the connected components of simple Artinian rings are generalized to larger ring classes, particularly, to semisimple Artinian and semiprime two-sided Goldie rings. Also the existence of isolated vertices in the graphs of the above ring classes is considered, and the behavior of the diameter function under taking a direct sum for pairs of arbitrary rings is studied. 
@article{ZNSL_2022_514_a8,
     author = {O. V. Markova and D. Yu. Novochadov},
     title = {Orthogonality graphs of direct sums of rings and semisimple {Artinian} rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--166},
     publisher = {mathdoc},
     volume = {514},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a8/}
}
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O. V. Markova; D. Yu. Novochadov. Orthogonality graphs of direct sums of rings and semisimple Artinian rings. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 138-166. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a8/