Geodesic
Behavior of the binary rank of a graph when vertices and edges are added
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2021), pp. 21-26

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We consider the issue of changing the binary rank of the adjacency matrix of a simple graph under adding vertices and some edges. The number of edges that appear after adding a vertex is not constant. 
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     author = {S. Yu. Bezgodova and D. P. Ilyutko},
     title = {Behavior of the binary rank of a graph when vertices and edges are added},
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S. Yu. Bezgodova; D. P. Ilyutko. Behavior of the binary rank of a graph when vertices and edges are added. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2021), pp. 21-26. http://geodesic.mathdoc.fr/item/VMUMM_2021_6_a3/