Geodesic
Minimum rank of a tree over an arbitrary field
The electronic journal of linear algebra, Tome 16 (2007), pp. 183-186.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For a field F and graph G of order n, the minimum rank of G over F is defined to be the smallest possible rank over all symmetric matrices A 2 F n*n whose (i, j)th entry (for i 6= j) is nonzero whenever ${i, j}$ is an edge in G and is zero otherwise. It is shown that the minimum rank of a tree is independent of the field.
Classification : 05C50, 15A18
Keywords: minimum rank, tree, graph, field, path, symmetric matrix 
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     title = {Minimum rank of a tree over an arbitrary field},
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Chenette, Nathan L.; Droms, Sean V.; Hogben, Leslie; Mikkelson, Rana; Pryporova, Olga. Minimum rank of a tree over an arbitrary field. The electronic journal of linear algebra, Tome 16 (2007), pp. 183-186. http://geodesic.mathdoc.fr/item/ELA_2007__16__a22/