Geodesic
Graphs defined by orthogonality
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 49-80

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The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings, the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices over an arbitrary field are computed. 
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     author = {B. R. Bakhadly and A. E. Guterman and O. V. Markova},
     title = {Graphs defined by orthogonality},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a4/}
}
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B. R. Bakhadly; A. E. Guterman; O. V. Markova. Graphs defined by orthogonality. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 49-80. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a4/