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ADDITIVE AUTOMORPHISMS OF REGULAR MATRIX GRAPH
Journal of Mathematical Sciences. 2026. Vol. 299. No. 6.
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| > 4 and m, n ≥ 2, all additive automorphisms of the regular graphs are characterized. Furthermore, it is proved that any automorphism of the regular graph preserves the rank distance d(A, B) = rk(A − B).
Keywords: regular graphAutomorphisms of graphsрегулярный граф кольца матрицАвтоморфизмы графаrectangular matricesпрямоугольные матрицы
Publication based on the results of:
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