Geodesic
Application of graphs to the Gaussian elimination method
Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 72-79

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Certain algebraic operations (in the Boolean sense) are developed for directed graphs. Nonsingular and inverse graphs are defined and some of their characteristics are derived. The results are applied for the Gaussian elimination process. 
@article{ZNSL_1976_58_a8,
     author = {M. Fidler},
     title = {Application of graphs to the {Gaussian} elimination method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--79},
     publisher = {mathdoc},
     volume = {58},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a8/}
}
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M. Fidler. Application of graphs to the Gaussian elimination method. Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 72-79. http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a8/