ELA, Volume 16, pp. 183-186, July 2007, abstract.

Minimum Rank of a Tree over an Arbitrary Field

Nathan L. Chenette, Sean V. Droms, Leslie Hogben,
Rana Mikkelson, and Olga Pryporova

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 nxn matrices A whose (i,j)th entry
(for i not equal to 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.